<PAGE>   1
 
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 6, 1998
 
                                                        REGISTRATION NO.
================================================================================
 
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549
                            ------------------------
 
                                    FORM S-8
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                            ------------------------
 
                               DIME BANCORP, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 
<TABLE>
<S>                                            <C>
                  DELAWARE                                      11-3197414
       (STATE OR OTHER JURISDICTION OF                       (I.R.S. EMPLOYER
       INCORPORATION OR ORGANIZATION)                       IDENTIFICATION NO.)
    589 FIFTH AVENUE, NEW YORK, NEW YORK                           10017
  (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                      (ZIP CODE)
</TABLE>
 
                  DIME BANCORP, INC. STOCK INCENTIVE PLAN AND
                  DIME BANCORP, INC. 1991 STOCK INCENTIVE PLAN
                            (FULL TITLE OF THE PLAN)
 
                              JAMES E. KELLY, ESQ.
                                GENERAL COUNSEL
                   589 FIFTH AVENUE, NEW YORK, NEW YORK 10017
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)
 
                                 (212) 326-6170
         (TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE)
 
                            ------------------------
 
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<CAPTION>
============================================================================================================
                                                      PROPOSED             PROPOSED
    TITLE OF SECURITIES         AMOUNT TO BE      MAXIMUM OFFERING     MAXIMUM AGGREGATE       AMOUNT OF
      TO BE REGISTERED           REGISTERED       PRICE PER SHARE*      OFFERING PRICE     REGISTRATION FEE
------------------------------------------------------------------------------------------------------------
<S>                           <C>                <C>                  <C>                  <C>
Common stock, par value $.01
  per share.................      5,000,000            $29.72            $148,600,000         $43,837.00
============================================================================================================
</TABLE>
 
* In accordance with Rule 457(c) and (h), the Maximum Aggregate Offering Price
  and Registration Fee have been computed as follows: (a) the price per share of
  the Common Stock of Dime Bancorp, Inc. (the "Company") has been based on the
  average of the high and low prices for the Common Stock of the Company as
  reported on the New York Stock Exchange on April 29, 1998, and (b) using such
  price per share, the aggregate amount of the Offering Price was then
  calculated on the basis of the aggregate amount of shares of Common Stock of
  the Company issuable in connection with the Dime Bancorp, Inc. 1991 Stock
  Incentive Plan.
 
  Pursuant to Rule 429 under the Securities Act of 1933, as amended, this
  Registration Statement also covers the shares of Common Stock previously
  registered under Registration Statement Nos. 33-88552 and 333-04477.
================================================================================
<PAGE>   2
 
                INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE
 
     The following documents previously filed with the Securities and Exchange
Commission (the "Commission") are incorporated by reference:
 
          (i) The Company's Registration Statement on Form 8-A as filed with the
     Commission on January 10, 1995, which includes a description of the Common
     Stock;
 
          (ii) The Company's Registration Statement on Form S-8 No. 33-88552 as
     filed with the Commission on January 18, 1995;
 
          (iii) The Company's Registration Statement on Form S-8 No. 333-04477
     as filed with the Commission on May 24, 1996; and
 
          (iv) The Company's Annual Report on Form 10-K for the year ended
     December 31, 1997.
 
     All documents subsequently filed by the Company pursuant to Sections 13(a),
13(c), 14, and 15(d) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), prior to the filing of any post-effective amendment which
indicates that all stock offered has been sold or which deregisters all stock
then remaining unsold, shall be deemed to be incorporated by reference in this
Registration Statement and to be a part hereof from the date of their filing.
Any statement contained in a document incorporated by reference herein shall be
deemed to be modified or superseded for purposes of this Registration Statement
to the extent that a statement contained herein or in any other subsequently
filed document which also is or is deemed to be incorporated by reference herein
modifies or supersedes such statement. Any such statement so modified or
superseded shall not be deemed, except as so modified or superseded, to
constitute a part of this Registration Statement.
<PAGE>   3
 
                                   SIGNATURES
 
     The Registrant.  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 New York, State of New York, on this 6th day of
May, 1998.
 
                                          DIME BANCORP, INC.
                                          (Registrant)
 
                                          By:     /s/ LAWRENCE J. TOAL
                                            ------------------------------------
                                            Lawrence J. Toal
                                            Chief Executive Officer, President
                                            and Chief Operating Officer
 
     Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the following
capacities as of May 6, 1998.
 
<TABLE>
<CAPTION>
                     SIGNATURE                                   TITLE
                     ---------                                   -----
<S>                                                     <C>
 
               /s/ LAWRENCE J. TOAL                     Chief Executive Officer, President, Chief      
---------------------------------------------------      Operating Officer and Chairman of the Board 
                 Lawrence J. Toal                        (Principal Executive Officer)
 
              /s/ JAMES M. LARGE, JR.                   A Director 
---------------------------------------------------
                James M. Large, Jr.
 
               /s/ DERRICK D. CEPHAS                    A Director 
---------------------------------------------------
                 Derrick D. Cephas
 
               /s/ FREDERICK C. CHEN                    A Director 
---------------------------------------------------
                 Frederick C. Chen
 
             /s/ J. BARCLAY COLLINS II                  A Director 
---------------------------------------------------
               J. Barclay Collins II
 
             /s/ RICHARD W. DALRYMPLE                   A Director
---------------------------------------------------
               Richard W. Dalrymple
 
                /s/ JAMES F. FULTON                     A Director 
---------------------------------------------------
                  James F. Fulton
 
               /s/ VIRGINIA M. KOPP                     A Director 
---------------------------------------------------
                 Virginia M. Kopp
 
                 /s/ JOHN MORNING                       A Director
---------------------------------------------------
                   John Morning
 
           /s/ MARGARET G. OSMER-MCQUADE                A Director
---------------------------------------------------
             Margaret G. Osmer-McQuade

            /s/ SALLY HERNANDEZ-PINERO                  A Director
---------------------------------------------------
              Sally Hernandez-Pinero
 
              /s/ DR. PAUL A. QUALBEN                   A Director              
---------------------------------------------------
                Dr. Paul A. Qualben
 
             /s/ EUGENE G. SCHULZ, JR.                  A Director              
---------------------------------------------------
               Eugene G. Schulz, Jr.
 
                 /s/ HOWARD SMITH                       A Director       
---------------------------------------------------
                   Howard Smith
 
              /s/ DR. NORMAN R. SMITH                   A Director   
---------------------------------------------------
                Dr. Norman R. Smith
 
                 /s/ IRA T. WENDER                      A Director       
---------------------------------------------------
                   Ira T. Wender
 
             /s/ ANTHONY R. BURRIESCI                   Chief Financial Officer
---------------------------------------------------
               Anthony R. Burriesci
 
              /s/ HAROLD E. REYNOLDS                    Controller
---------------------------------------------------
                Harold E. Reynolds
</TABLE>                                                        
<PAGE>   4
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
                                                                            SEQUENTIALLY
                                                                              NUMBERED
EXHIBIT NO.                                                                     PAGE
-----------                                                                 ------------
<S>           <C>                                                           <C>
    4.1       Copies of Amendments to the Dime Bancorp, Inc. 1991 Stock
              incentive Plan, effective as of October 1, 1996, September
              19, 1997 and March 27, 1997.................................        5
    5.1       Opinion of Counsel regarding the Legality of the Common
              Stock Being Registered by the Company.......................       13
   23.1       Consent of Counsel (included in Exhibit 5.1)................       13
   23.2       Consent of KPMG Peat Marwick LLP............................       15
</TABLE>
[{"type": "S-8", "sequence": "1", "description": "DIME BANCORP, INC.", "secsgml_size_bytes": 10943}]
{"company-data": {"conformed-name": "DIME BANCORP INC", "cik": "0000919568", "assigned-sic": "6035", "irs-number": "113197414", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-51941", "film-number": "98611587"}, "business-address": {"street1": "589 5TH AVE", "city": "NEW YORK", "state": "NY", "zip": "10017", "phone": "2123266170"}, "mail-address": {"street1": "589 FIFTH AVENUE", "city": "NEW YORK", "state": "NY", "zip": "10017"}}
1
 
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 6, 1998
 
                                                        REGISTRATION NO.
================================================================================
 
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549
                            ------------------------
 
                                    FORM S-8
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                            ------------------------
 
                               DIME BANCORP, INC.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
DELAWARE                                      11-3197414
       (STATE OR OTHER JURISDICTION OF                       (I.R.S. EMPLOYER
       INCORPORATION OR ORGANIZATION)                       IDENTIFICATION NO.)
    589 FIFTH AVENUE, NEW YORK, NEW YORK                           10017
  (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                      (ZIP CODE)
DIME BANCORP, INC. STOCK INCENTIVE PLAN AND
                  DIME BANCORP, INC. 1991 STOCK INCENTIVE PLAN
                            (FULL TITLE OF THE PLAN)
 
                              JAMES E. KELLY, ESQ.
                                GENERAL COUNSEL
                   589 FIFTH AVENUE, NEW YORK, NEW YORK 10017
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)
 
                                 (212) 326-6170
         (TELEPHONE NUMBER, INCLUDING AREA CODE, OF AGENT FOR SERVICE)
 
                            ------------------------
 
                        CALCULATION OF REGISTRATION FEE
============================================================================================================
                                                      PROPOSED             PROPOSED
    TITLE OF SECURITIES         AMOUNT TO BE      MAXIMUM OFFERING     MAXIMUM AGGREGATE       AMOUNT OF
      TO BE REGISTERED           REGISTERED       PRICE PER SHARE*      OFFERING PRICE     REGISTRATION FEE
------------------------------------------------------------------------------------------------------------
Common stock, par value $.01
  per share.................      5,000,000            $29.72            $148,600,000         $43,837.00
============================================================================================================
* In accordance with Rule 457(c) and (h), the Maximum Aggregate Offering Price
  and Registration Fee have been computed as follows: (a) the price per share of
  the Common Stock of Dime Bancorp, Inc. (the "Company") has been based on the
  average of the high and low prices for the Common Stock of the Company as
  reported on the New York Stock Exchange on April 29, 1998, and (b) using such
  price per share, the aggregate amount of the Offering Price was then
  calculated on the basis of the aggregate amount of shares of Common Stock of
  the Company issuable in connection with the Dime Bancorp, Inc. 1991 Stock
  Incentive Plan.
 
  Pursuant to Rule 429 under the Securities Act of 1933, as amended, this
  Registration Statement also covers the shares of Common Stock previously
  registered under Registration Statement Nos. 33-88552 and 333-04477.
================================================================================
2
 
                INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE
 
     The following documents previously filed with the Securities and Exchange
Commission (the "Commission") are incorporated by reference:
 
          (i) The Company's Registration Statement on Form 8-A as filed with the
     Commission on January 10, 1995, which includes a description of the Common
     Stock;
 
          (ii) The Company's Registration Statement on Form S-8 No. 33-88552 as
     filed with the Commission on January 18, 1995;
 
          (iii) The Company's Registration Statement on Form S-8 No. 333-04477
     as filed with the Commission on May 24, 1996; and
 
          (iv) The Company's Annual Report on Form 10-K for the year ended
     December 31, 1997.
 
     All documents subsequently filed by the Company pursuant to Sections 13(a),
13(c), 14, and 15(d) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), prior to the filing of any post-effective amendment which
indicates that all stock offered has been sold or which deregisters all stock
then remaining unsold, shall be deemed to be incorporated by reference in this
Registration Statement and to be a part hereof from the date of their filing.
Any statement contained in a document incorporated by reference herein shall be
deemed to be modified or superseded for purposes of this Registration Statement
to the extent that a statement contained herein or in any other subsequently
filed document which also is or is deemed to be incorporated by reference herein
modifies or supersedes such statement. Any such statement so modified or
superseded shall not be deemed, except as so modified or superseded, to
constitute a part of this Registration Statement.
3
 
                                   SIGNATURES
 
     The Registrant.  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 New York, State of New York, on this 6th day of
May, 1998.
 
                                          DIME BANCORP, INC.
                                          (Registrant)
 
                                          By:     /s/ LAWRENCE J. TOAL
                                            ------------------------------------
                                            Lawrence J. Toal
                                            Chief Executive Officer, President
                                            and Chief Operating Officer
 
     Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the following
capacities as of May 6, 1998.
SIGNATURE                                   TITLE
                     ---------                                   -----
/s/ LAWRENCE J. TOAL                     Chief Executive Officer, President, Chief      
---------------------------------------------------      Operating Officer and Chairman of the Board 
                 Lawrence J. Toal                        (Principal Executive Officer)
 
              /s/ JAMES M. LARGE, JR.                   A Director 
---------------------------------------------------
                James M. Large, Jr.
 
               /s/ DERRICK D. CEPHAS                    A Director 
---------------------------------------------------
                 Derrick D. Cephas
 
               /s/ FREDERICK C. CHEN                    A Director 
---------------------------------------------------
                 Frederick C. Chen
 
             /s/ J. BARCLAY COLLINS II                  A Director 
---------------------------------------------------
               J. Barclay Collins II
 
             /s/ RICHARD W. DALRYMPLE                   A Director
---------------------------------------------------
               Richard W. Dalrymple
 
                /s/ JAMES F. FULTON                     A Director 
---------------------------------------------------
                  James F. Fulton
 
               /s/ VIRGINIA M. KOPP                     A Director 
---------------------------------------------------
                 Virginia M. Kopp
 
                 /s/ JOHN MORNING                       A Director
---------------------------------------------------
                   John Morning
 
           /s/ MARGARET G. OSMER-MCQUADE                A Director
---------------------------------------------------
             Margaret G. Osmer-McQuade

            /s/ SALLY HERNANDEZ-PINERO                  A Director
---------------------------------------------------
              Sally Hernandez-Pinero
 
              /s/ DR. PAUL A. QUALBEN                   A Director              
---------------------------------------------------
                Dr. Paul A. Qualben
 
             /s/ EUGENE G. SCHULZ, JR.                  A Director              
---------------------------------------------------
               Eugene G. Schulz, Jr.
 
                 /s/ HOWARD SMITH                       A Director       
---------------------------------------------------
                   Howard Smith
 
              /s/ DR. NORMAN R. SMITH                   A Director   
---------------------------------------------------
                Dr. Norman R. Smith
 
                 /s/ IRA T. WENDER                      A Director       
---------------------------------------------------
                   Ira T. Wender
 
             /s/ ANTHONY R. BURRIESCI                   Chief Financial Officer
---------------------------------------------------
               Anthony R. Burriesci
 
              /s/ HAROLD E. REYNOLDS                    Controller
---------------------------------------------------
                Harold E. Reynolds
4
 
                                 EXHIBIT INDEX
SEQUENTIALLY
                                                                              NUMBERED
EXHIBIT NO.                                                                     PAGE
-----------                                                                 ------------
4.1       Copies of Amendments to the Dime Bancorp, Inc. 1991 Stock
              incentive Plan, effective as of October 1, 1996, September
              19, 1997 and March 27, 1997.................................        5
    5.1       Opinion of Counsel regarding the Legality of the Common
              Stock Being Registered by the Company.......................       13
   23.1       Consent of Counsel (included in Exhibit 5.1)................       13
   23.2       Consent of KPMG Peat Marwick LLP............................       15