<PAGE>   1


                                                       Registration No. 33-_____

    As filed with the Securities and Exchange Commission on February 13, 1995
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

                            _______________________

                                    FORM S-8
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                            _______________________

                           NOBLE DRILLING CORPORATION
             (Exact name of registrant as specified in its charter)



            DELAWARE                                     73-0374541
  (State or other jurisdiction              (I.R.S. Employer Identification No.)
of incorporation or organization)

10370 RICHMOND AVENUE, SUITE 400                            
        HOUSTON, TEXAS                                      77042
(Address of Principal Executive Offices)                  (Zip Code)

                            _______________________

                  NOBLE DRILLING CORPORATION 1991 STOCK OPTION
                           AND RESTRICTED STOCK PLAN
                            (Full title of the Plan)
                            _______________________


                   JAMES C. DAY                                Copy to:
   CHAIRMAN, PRESIDENT AND CHIEF EXECUTIVE OFFICER         ROBERT D. CAMPBELL
           NOBLE DRILLING CORPORATION                    THOMPSON & KNIGHT, P.C.
        10370 RICHMOND AVENUE, SUITE 400                   1700 PACIFIC AVENUE
            HOUSTON, TEXAS  77042                              SUITE 3300
     (Name and address of agent for service)               DALLAS, TEXAS  75201
                                                              (214) 969-1353
                 (713) 974-3131
           (Telephone number, including
          area code, of agent for service)

                        CALCULATION OF REGISTRATION FEE


<TABLE>
<CAPTION>
===========================================================================================================
       Title of                                    Proposed          Proposed Maximum           Amount
      Securities              Amount                Maximum              Aggregate                of
         to be                 to be            Offering Price           Offering            Registration
      Registered           Registered(1)         per Share(2)            Price(2)                 Fee
- -----------------------------------------------------------------------------------------------------------
    <S>                      <C>                   <C>                 <C>                     <C>
     Common Stock,           3,300,000
    par value $.10            shares               $5.25                $17,325,000             $5,975
       per share
===========================================================================================================
</TABLE>

(1) Pursuant to Rule 416 under the Securities Act of 1933, shares issuable upon
    any stock split, stock dividend or similar transaction with respect to
    these shares are also being registered hereunder.

(2) Estimated solely for the purpose of determining the registration fee
    pursuant to Rule 457(h) on the basis of the average of the high and low
    sales prices of the Common Stock reported in the consolidated reporting
    system for NASDAQ National Market System securities on February 8, 1995.
================================================================================
<PAGE>   2

                                     PART I

                       INCORPORATION OF CONTENTS OF PRIOR
                             REGISTRATION STATEMENT


    The contents of Registration Statement No. 33-46724 relating to the Noble
Drilling Corporation 1991 Stock Option and Restricted Stock Plan (the "Plan")
filed by the Registrant with the Securities and Exchange Commission on April 1,
1992 (the "Prior Registration Statement") are incorporated herein by reference
pursuant to General Instruction E to Form S-8.  The purpose of this
Registration Statement is to register 3,300,000 additional shares of Common
Stock of the Registrant for offer and sale pursuant to the Plan.


                                    PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT



Item 6.  Indemnification of Directors and Officers.

    The Registrant is a Delaware corporation.  Under Section 145 of the General
Corporation Law of the State of Delaware, the Registrant has the power to
indemnify its directors and officers, subject to certain limitations.

    Reference is made to Article VI of the Bylaws of the Registrant, which
provides for indemnification of directors and officers of the Registrant under
certain circumstances.

    Pursuant to the General Corporation Law of the State of Delaware, the
Certificate of Incorporation of the Registrant limits the personal liability of
the directors of the Registrant to the Registrant or its stockholders for
monetary damages for breach of fiduciary duty under certain circumstances.

    The Registrant also maintains insurance to protect itself and its
directors, officers, employees and agents against expenses, liabilities and
losses incurred by such persons in connection with their service in the
foregoing capacities.

    The foregoing summaries are necessarily subject to the complete text of the
statute, bylaw, certificate of incorporation and insurance policy referred to
above and are qualified in their entirety by reference thereto.





                                      -1-
<PAGE>   3

Item 8.  Exhibits.

    In addition to the exhibits filed with or incorporated by reference in the
Prior Registration Statement, the following documents are filed or incorporated
by reference as exhibits to this Registration Statement:

<TABLE>
<CAPTION>
Exhibit
Number          Description
- ------          -----------
<S>          <C>
4.1          Noble Drilling Corporation 1991 Stock Option and Restricted Stock Plan, as amended and restated through September 15,
             1994.

5.1          Opinion of Thompson & Knight, A Professional Corporation, regarding 3,300,000 shares of Common Stock of the Registrant.

23.1         Consent of Thompson & Knight, A Professional Corporation (contained in its opinion filed herewith as Exhibit 5.1).    
                                                                                                                                   
23.2         Consent of Arthur Andersen LLP.                                                                                       
                                                                                                                                   
23.3         Consent of KPMG Peat Marwick LLP.                                                                                     
                                                                                                                                   
24.1         Power of Attorney (included on the signature page of this Registration Statement).                                    
</TABLE>         





                                      -2-
<PAGE>   4

                                   SIGNATURES


    Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, State of Texas, on the 13th day of February,
1995.


                     NOBLE DRILLING CORPORATION
                     (Registrant)



                     By:  JAMES C. DAY
                          James C. Day
                          Chairman, President and Chief Executive Officer


    Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the date indicated.

    Each person whose signature appears below constitutes and appoints James C.
Day and Byron L. Welliver, and each of them (with full power to each of them to
act alone), his true and lawful attorney-in-fact and agent, with full power of
substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities to sign on his behalf individually and in each capacity
stated below any amendment, including post-effective amendments, to this
Registration Statement, and to file the same, with all exhibits thereto and
other documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in and about the premises, as fully to all
intents and purposes as he might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents and either of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

<TABLE>
<CAPTION>
Signature                              Title                                              Date
- ---------                              -----                                              ----
<S>                                    <C>                                                <C>
JAMES C. DAY                           Chairman, President and Chief Executive            February 13, 1995
- ----------------------------------     Officer and Director                                               
James C. Day                           (Principal Executive Officer)
                                                                    
</TABLE>                               





                                      -3-
<PAGE>   5
<TABLE>
<CAPTION>
Signature                              Title                                              Date
- ---------                              -----                                              ----
<S>                                    <C>                                                <C>
BYRON L. WELLIVER                      Senior Vice President -                            February 13, 1995
- ----------------------------------     Finance, Treasurer and Controller                                  
Byron L. Welliver                      (Principal Financial and Accounting
                                       Officer)                           
                                                                          
                                       
MICHAEL A. CAWLEY                      Director                                           February 13, 1995
- ----------------------------------                                                                        
Michael A. Cawley


LAWRENCE J. CHAZEN                     Director                                           February 13, 1995
- ----------------------------------                                                                        
Lawrence J. Chazen


TOMMY C. CRAIGHEAD                     Director                                           February 13, 1995
- ------------------                                                                                        
Tommy C. Craighead


JAMES L. FISHEL                        Director                                           February 13, 1995
- ----------------------------------                                                                        
James L. Fishel


JOHNNIE W. HOFFMAN                     Director                                           February 13, 1995
- ----------------------------------                                                                        
Johnnie W. Hoffman


MARC E. LELAND                         Director                                           February 13, 1995
- ----------------------------------                                                                        
Marc E. Leland


                                       Director
- ----------------------------------             
John F. Snodgrass


BILL M. THOMPSON                       Director                                           February 13, 1995
- ----------------------------------                                                                        
Bill M. Thompson
</TABLE>





                                      -4-
<PAGE>   6
                               INDEX TO EXHIBITS


<TABLE>
<CAPTION>
      Exhibit
      Number                                        Exhibit
      ------                                        -------
        <S>               <C>
        4.1               Noble Drilling Corporation 1991 Stock Option and Restricted                  
                          Stock Plan, as amended and restated through September 15,                    
                          1994.                                                                        
                                                                                                       
        5.1               Opinion of Thompson & Knight, A Professional Corporation,                    
                          regarding 3,300,000 shares of Common Stock.                                  
                                                                                                       
       23.1               Consent of Thompson & Knight, A Professional Corporation                     
                          (contained in its opinion filed herewith as Exhibit 5.1).                    
                                                                                                       
       23.2               Consent of Arthur Andersen LLP.                                              
                                                                                                       
       23.3               Consent of KPMG Peat Marwick LLP.                                            
                                                                                                       
       24.1               Power of Attorney (included on the signature page of this                    
                          Registration Statement).                                                     
                                                                                                       
</TABLE>                  





                                      -5-
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 14884}]
{"company-data": {"conformed-name": "NOBLE DRILLING CORP", "cik": "0000777201", "assigned-sic": "1381", "irs-number": "730374541", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "033-57675", "film-number": "95509644"}, "business-address": {"street1": "10370 RICHMOND AVE STE 400", "city": "HOUSTON", "state": "TX", "zip": "77042", "phone": "7139743131"}, "mail-address": {"street1": "10370 RICHMOND AVE", "street2": "STE 400", "city": "HOUSTON", "state": "TX", "zip": "77042"}}
1

                                                       Registration No. 33-_____

    As filed with the Securities and Exchange Commission on February 13, 1995
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

                            _______________________

                                    FORM S-8
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                            _______________________

                           NOBLE DRILLING CORPORATION
             (Exact name of registrant as specified in its charter)

            DELAWARE                                     73-0374541
  (State or other jurisdiction              (I.R.S. Employer Identification No.)
of incorporation or organization)

10370 RICHMOND AVENUE, SUITE 400                            
        HOUSTON, TEXAS                                      77042
(Address of Principal Executive Offices)                  (Zip Code)

                            _______________________

                  NOBLE DRILLING CORPORATION 1991 STOCK OPTION
                           AND RESTRICTED STOCK PLAN
                            (Full title of the Plan)
                            _______________________

                   JAMES C. DAY                                Copy to:
   CHAIRMAN, PRESIDENT AND CHIEF EXECUTIVE OFFICER         ROBERT D. CAMPBELL
           NOBLE DRILLING CORPORATION                    THOMPSON & KNIGHT, P.C.
        10370 RICHMOND AVENUE, SUITE 400                   1700 PACIFIC AVENUE
            HOUSTON, TEXAS  77042                              SUITE 3300
     (Name and address of agent for service)               DALLAS, TEXAS  75201
                                                              (214) 969-1353
                 (713) 974-3131
           (Telephone number, including
          area code, of agent for service)

                        CALCULATION OF REGISTRATION FEE
===========================================================================================================
       Title of                                    Proposed          Proposed Maximum           Amount
      Securities              Amount                Maximum              Aggregate                of
         to be                 to be            Offering Price           Offering            Registration
      Registered           Registered(1)         per Share(2)            Price(2)                 Fee
- -----------------------------------------------------------------------------------------------------------
Common Stock,           3,300,000
    par value $.10            shares               $5.25                $17,325,000             $5,975
       per share
===========================================================================================================
(1) Pursuant to Rule 416 under the Securities Act of 1933, shares issuable upon
    any stock split, stock dividend or similar transaction with respect to
    these shares are also being registered hereunder.

(2) Estimated solely for the purpose of determining the registration fee
    pursuant to Rule 457(h) on the basis of the average of the high and low
    sales prices of the Common Stock reported in the consolidated reporting
    system for NASDAQ National Market System securities on February 8, 1995.
================================================================================
2

                                     PART I

                       INCORPORATION OF CONTENTS OF PRIOR
                             REGISTRATION STATEMENT

    The contents of Registration Statement No. 33-46724 relating to the Noble
Drilling Corporation 1991 Stock Option and Restricted Stock Plan (the "Plan")
filed by the Registrant with the Securities and Exchange Commission on April 1,
1992 (the "Prior Registration Statement") are incorporated herein by reference
pursuant to General Instruction E to Form S-8.  The purpose of this
Registration Statement is to register 3,300,000 additional shares of Common
Stock of the Registrant for offer and sale pursuant to the Plan.

                                    PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

Item 6.  Indemnification of Directors and Officers.

    The Registrant is a Delaware corporation.  Under Section 145 of the General
Corporation Law of the State of Delaware, the Registrant has the power to
indemnify its directors and officers, subject to certain limitations.

    Reference is made to Article VI of the Bylaws of the Registrant, which
provides for indemnification of directors and officers of the Registrant under
certain circumstances.

    Pursuant to the General Corporation Law of the State of Delaware, the
Certificate of Incorporation of the Registrant limits the personal liability of
the directors of the Registrant to the Registrant or its stockholders for
monetary damages for breach of fiduciary duty under certain circumstances.

    The Registrant also maintains insurance to protect itself and its
directors, officers, employees and agents against expenses, liabilities and
losses incurred by such persons in connection with their service in the
foregoing capacities.

    The foregoing summaries are necessarily subject to the complete text of the
statute, bylaw, certificate of incorporation and insurance policy referred to
above and are qualified in their entirety by reference thereto.

                                      -1-
3

Item 8.  Exhibits.

    In addition to the exhibits filed with or incorporated by reference in the
Prior Registration Statement, the following documents are filed or incorporated
by reference as exhibits to this Registration Statement:
Exhibit
Number          Description
- ------          -----------
4.1          Noble Drilling Corporation 1991 Stock Option and Restricted Stock Plan, as amended and restated through September 15,
             1994.

5.1          Opinion of Thompson & Knight, A Professional Corporation, regarding 3,300,000 shares of Common Stock of the Registrant.

23.1         Consent of Thompson & Knight, A Professional Corporation (contained in its opinion filed herewith as Exhibit 5.1).    
                                                                                                                                   
23.2         Consent of Arthur Andersen LLP.                                                                                       
                                                                                                                                   
23.3         Consent of KPMG Peat Marwick LLP.                                                                                     
                                                                                                                                   
24.1         Power of Attorney (included on the signature page of this Registration Statement).
-2-
4

                                   SIGNATURES

    Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, State of Texas, on the 13th day of February,
1995.

                     NOBLE DRILLING CORPORATION
                     (Registrant)

                     By:  JAMES C. DAY
                          James C. Day
                          Chairman, President and Chief Executive Officer

    Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the date indicated.

    Each person whose signature appears below constitutes and appoints James C.
Day and Byron L. Welliver, and each of them (with full power to each of them to
act alone), his true and lawful attorney-in-fact and agent, with full power of
substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities to sign on his behalf individually and in each capacity
stated below any amendment, including post-effective amendments, to this
Registration Statement, and to file the same, with all exhibits thereto and
other documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each and every act and thing
requisite and necessary to be done in and about the premises, as fully to all
intents and purposes as he might or could do in person, hereby ratifying and
confirming all that said attorneys-in-fact and agents and either of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.
Signature                              Title                                              Date
- ---------                              -----                                              ----
JAMES C. DAY                           Chairman, President and Chief Executive            February 13, 1995
- ----------------------------------     Officer and Director                                               
James C. Day                           (Principal Executive Officer)
-3-
5
Signature                              Title                                              Date
- ---------                              -----                                              ----
BYRON L. WELLIVER                      Senior Vice President -                            February 13, 1995
- ----------------------------------     Finance, Treasurer and Controller                                  
Byron L. Welliver                      (Principal Financial and Accounting
                                       Officer)                           
                                                                          
                                       
MICHAEL A. CAWLEY                      Director                                           February 13, 1995
- ----------------------------------                                                                        
Michael A. Cawley

LAWRENCE J. CHAZEN                     Director                                           February 13, 1995
- ----------------------------------                                                                        
Lawrence J. Chazen

TOMMY C. CRAIGHEAD                     Director                                           February 13, 1995
- ------------------                                                                                        
Tommy C. Craighead

JAMES L. FISHEL                        Director                                           February 13, 1995
- ----------------------------------                                                                        
James L. Fishel

JOHNNIE W. HOFFMAN                     Director                                           February 13, 1995
- ----------------------------------                                                                        
Johnnie W. Hoffman

MARC E. LELAND                         Director                                           February 13, 1995
- ----------------------------------                                                                        
Marc E. Leland

                                       Director
- ----------------------------------             
John F. Snodgrass

BILL M. THOMPSON                       Director                                           February 13, 1995
- ----------------------------------                                                                        
Bill M. Thompson
-4-
6
                               INDEX TO EXHIBITS
Exhibit
      Number                                        Exhibit
      ------                                        -------
4.1               Noble Drilling Corporation 1991 Stock Option and Restricted                  
                          Stock Plan, as amended and restated through September 15,                    
                          1994.                                                                        
                                                                                                       
        5.1               Opinion of Thompson & Knight, A Professional Corporation,                    
                          regarding 3,300,000 shares of Common Stock.                                  
                                                                                                       
       23.1               Consent of Thompson & Knight, A Professional Corporation                     
                          (contained in its opinion filed herewith as Exhibit 5.1).                    
                                                                                                       
       23.2               Consent of Arthur Andersen LLP.                                              
                                                                                                       
       23.3               Consent of KPMG Peat Marwick LLP.                                            
                                                                                                       
       24.1               Power of Attorney (included on the signature page of this                    
                          Registration Statement).
-5-