<PAGE>   1
As filed on July 30, 1998                             Registration No. ___-_____

--------------------------------------------------------------------------------
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549
     ----------------------------------------------------------------------

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

                            ABERCROMBIE & FITCH CO.
     ----------------------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)


             Delaware                               31-1469076
---------------------------------      -----------------------------------
(State or Other Jurisdiction of          (IRS Employer Identification No.)
Incorporation or Organization)


        Four Limited Parkway East, Reynoldsburg, Ohio             43068
   -------------------------------------------------------------------------
          (Address of Principal Executive Offices)              (Zip Code)


    ABERCROMBIE & FITCH CO. 1996 STOCK OPTION AND PERFORMANCE INCENTIVE PLAN
    ------------------------------------------------------------------------
                               (1998 RESTATEMENT)
                               ------------------
      ABERCROMBIE & FITCH CO. 1996 STOCK PLAN FOR NON-ASSOCIATE DIRECTORS
      -------------------------------------------------------------------
                               (1998 RESTATEMENT)
                               ------------------
                           (Full Title of the Plans)

                                SETH R. JOHNSON
                   Vice President and Chief Financial Officer
                            Abercrombie & Fitch Co.
                           Four Limited Parkway East
                            Reynoldsburg, Ohio 43068
                                 (614) 577-6500
          -----------------------------------------------------------
           (Name, Address and Telephone Number of Agent for Service)


                        CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>

=========================================================================================================
                                             Proposed Maximum      Proposed Maximum
Title of Securities   Amount to be          Offering Price per    Aggregate Offering       Amount of
to be Registered      Registered(1)              Share(2)              Price(2)         Registration Fee

---------------------------------------------------------------------------------------------------------
<S>                   <C>                   <C>                   <C>                   <C>
Class A Common
Stock, $.01 par
value               2,100,000 shares            $45.59375             $95,746,875           $28,245.33
=========================================================================================================
</TABLE>

     (1) Of this number, 2,000,000 shares are being registered for issuance
under the 1996 Stock Option and Performance Incentive Plan (1998 Restatement)
and 100,000 shares are being registered for issuance under the 1996 Stock Plan
for Non-Associate Directors (1998 Restatement).

     (2) Estimated solely for the purpose of calculating the registration fee
pursuant to Rule 457(c) and (h) under the Securities Act of 1933, as amended,
based upon the average of the high and low prices reported in the New York Stock
Exchange consolidated reporting system as of July 28, 1998.

                        --------------------------------



<PAGE>   2


                     REGISTRATION OF ADDITIONAL SECURITIES

     Pursuant to General Instruction E, this Registration Statement on Form S-8
is filed by Abercrombie & Fitch Co. (the "Registrant") to register additional
securities under the Abercrombie & Fitch Co. 1996 Stock Plan for Non-Associate
Directors and the 1996 Stock Option and Performance Incentive Plan (the "Plans")
which are covered by and filed as exhibits to the Registrant's Registration
Statements on Form S-8 (Nos. 333-15941 and 333-15945, respectively).  The
additional securities are to be issued pursuant to restatements of the Plans
approved by the Executive Committee of the Registrant's Board of Directors on
May 18, 1998 and by the Registrant's shareholders on July 16, 1998.  The
contents of Registration Statements No. 333-15941 and 333-15945 are incorporated
herein by reference.






                                       2
<PAGE>   3



                                    PART II

                 INFORMATION REQUIRED IN REGISTRATION STATEMENT

Item 5.  Interests of Named Experts and Counsel.

         The validity of the issuance of the shares of Class A Common Stock of
the Registrant being registered on this Registration Statement on Form S-8 will
be passed upon for the Registrant by Vorys, Sater, Seymour and Pease LLP, 52
East Gay Street, P.O. Box 1008, Columbus, Ohio  43216-1008.  Douglas L.
Williams, a director of the Registrant, is a partner in such firm.  As of July
6, 1998, members of Vorys, Sater, Seymour and Pease LLP and attorneys employed
thereby, together with members of their immediate families, beneficially owned
an aggregate of 1,300 shares of Class A Common Stock of the Registrant.

Item 8.  Exhibits.

         See Exhibit Index on page 6.

Item 9.  Undertakings.

         Incorporated herein by reference to Registration Statements Nos.
333-15941 and 333-15945.













                                       3


<PAGE>   4


                                   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 Reynoldsburg, State of Ohio, on July 29, 1998.

                            ABERCROMBIE & FITCH CO.
                            (The Registrant)

                            By /s/ Seth R. Johnson
                              ---------------------
                              Seth R. Johnson,
                              Vice President and Chief Financial Officer

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated on July 29, 1998.


Signature                           Title
---------                           -----

             *
----------------------------- 
Michael S.  Jeffries                Chairman of the Board of Directors and
                                    Chief Executive Officer
                                    (Principal Executive Officer)

 /s/ Seth R. Johnson
-----------------------------       Vice President and Chief Financial Officer
Seth R.  Johnson                    and Director (Principal Financial and
                                    Accounting Officer)
             *
-----------------------------       Director
George Foos
             *
-----------------------------       Director
John A. Golden
             *
-----------------------------       Director
John W. Kessler
             *
-----------------------------       Director
Sam N. Shahid, Jr.
             *
-----------------------------       Director
Douglas L. Williams



                                       4


<PAGE>   5



     *Seth R. Johnson, by signing his name hereto, signs this document on
behalf of the persons indicated above pursuant to powers of attorney duly
executed by such persons.


                               By /s/ Seth R. Johnson
                                 -------------------------
                                  Seth R. Johnson,
                                  Attorney-in-Fact











                                       5
<PAGE>   6

                                 EXHIBIT INDEX


     The following exhibits are filed as part of this Registration Statement:


                                    Exhibit

4.1   Amended and Restated Certificate of Incorporation of the Registrant
      incorporated by reference to Exhibit 3.1 of the Registrant's quarterly
      report on Form 10-Q for the quarter ended November 2, 1996.

4.2   Form of Bylaws of the Registrant incorporated by reference to Exhibit 3.1
      of the Registrant's quarterly report on Form 10-Q for the quarter ended
      November 2, 1996.

5.1   Legal opinion of Vorys, Sater, Seymour and Pease LLP.

15.1  Letter of PricewaterhouseCoopers LLP regarding Unaudited Interim Financial
      Information.

23.1  Consent of PricewaterhouseCoopers LLP.

23.2  Consent of Vorys, Sater, Seymour and Pease LLP (included in the opinion 
      filed as Exhibit 5.1).

24.1  Power of Attorney.







                                       6
[{"type": "S-8", "sequence": "1", "description": "REGISTRATION STATEMENT", "secsgml_size_bytes": 9096}]
{"company-data": {"conformed-name": "ABERCROMBIE & FITCH CO /DE/", "cik": "0001018840", "assigned-sic": "5651", "irs-number": "311469076", "state-of-incorporation": "DE", "fiscal-year-end": "0131"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-60189", "film-number": "98674283"}, "business-address": {"street1": "FOUR LIMITED PARKWAY EAST", "city": "REYNOLDSBURG", "state": "OH", "zip": "43068", "phone": "6145776500"}, "mail-address": {"street1": "FOUR LIMITED PARKWAY EAST", "city": "COLUMBUS", "state": "OH", "zip": "43068"}}
1
As filed on July 30, 1998                             Registration No. ___-_____

--------------------------------------------------------------------------------
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549
     ----------------------------------------------------------------------

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

                            ABERCROMBIE & FITCH CO.
     ----------------------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)

             Delaware                               31-1469076
---------------------------------      -----------------------------------
(State or Other Jurisdiction of          (IRS Employer Identification No.)
Incorporation or Organization)

        Four Limited Parkway East, Reynoldsburg, Ohio             43068
   -------------------------------------------------------------------------
          (Address of Principal Executive Offices)              (Zip Code)

    ABERCROMBIE & FITCH CO. 1996 STOCK OPTION AND PERFORMANCE INCENTIVE PLAN
    ------------------------------------------------------------------------
                               (1998 RESTATEMENT)
                               ------------------
      ABERCROMBIE & FITCH CO. 1996 STOCK PLAN FOR NON-ASSOCIATE DIRECTORS
      -------------------------------------------------------------------
                               (1998 RESTATEMENT)
                               ------------------
                           (Full Title of the Plans)

                                SETH R. JOHNSON
                   Vice President and Chief Financial Officer
                            Abercrombie & Fitch Co.
                           Four Limited Parkway East
                            Reynoldsburg, Ohio 43068
                                 (614) 577-6500
          -----------------------------------------------------------
           (Name, Address and Telephone Number of Agent for Service)

                        CALCULATION OF REGISTRATION FEE
=========================================================================================================
                                             Proposed Maximum      Proposed Maximum
Title of Securities   Amount to be          Offering Price per    Aggregate Offering       Amount of
to be Registered      Registered(1)              Share(2)              Price(2)         Registration Fee

---------------------------------------------------------------------------------------------------------
Class A Common
Stock, $.01 par
value               2,100,000 shares            $45.59375             $95,746,875           $28,245.33
=========================================================================================================
(1) Of this number, 2,000,000 shares are being registered for issuance
under the 1996 Stock Option and Performance Incentive Plan (1998 Restatement)
and 100,000 shares are being registered for issuance under the 1996 Stock Plan
for Non-Associate Directors (1998 Restatement).

     (2) Estimated solely for the purpose of calculating the registration fee
pursuant to Rule 457(c) and (h) under the Securities Act of 1933, as amended,
based upon the average of the high and low prices reported in the New York Stock
Exchange consolidated reporting system as of July 28, 1998.

                        --------------------------------
2

                     REGISTRATION OF ADDITIONAL SECURITIES

     Pursuant to General Instruction E, this Registration Statement on Form S-8
is filed by Abercrombie & Fitch Co. (the "Registrant") to register additional
securities under the Abercrombie & Fitch Co. 1996 Stock Plan for Non-Associate
Directors and the 1996 Stock Option and Performance Incentive Plan (the "Plans")
which are covered by and filed as exhibits to the Registrant's Registration
Statements on Form S-8 (Nos. 333-15941 and 333-15945, respectively).  The
additional securities are to be issued pursuant to restatements of the Plans
approved by the Executive Committee of the Registrant's Board of Directors on
May 18, 1998 and by the Registrant's shareholders on July 16, 1998.  The
contents of Registration Statements No. 333-15941 and 333-15945 are incorporated
herein by reference.

                                       2
3

                                    PART II

                 INFORMATION REQUIRED IN REGISTRATION STATEMENT

Item 5.  Interests of Named Experts and Counsel.

         The validity of the issuance of the shares of Class A Common Stock of
the Registrant being registered on this Registration Statement on Form S-8 will
be passed upon for the Registrant by Vorys, Sater, Seymour and Pease LLP, 52
East Gay Street, P.O. Box 1008, Columbus, Ohio  43216-1008.  Douglas L.
Williams, a director of the Registrant, is a partner in such firm.  As of July
6, 1998, members of Vorys, Sater, Seymour and Pease LLP and attorneys employed
thereby, together with members of their immediate families, beneficially owned
an aggregate of 1,300 shares of Class A Common Stock of the Registrant.

Item 8.  Exhibits.

         See Exhibit Index on page 6.

Item 9.  Undertakings.

         Incorporated herein by reference to Registration Statements Nos.
333-15941 and 333-15945.

                                       3
4

                                   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 Reynoldsburg, State of Ohio, on July 29, 1998.

                            ABERCROMBIE & FITCH CO.
                            (The Registrant)

                            By /s/ Seth R. Johnson
                              ---------------------
                              Seth R. Johnson,
                              Vice President and Chief Financial Officer

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated on July 29, 1998.

Signature                           Title
---------                           -----

             *
----------------------------- 
Michael S.  Jeffries                Chairman of the Board of Directors and
                                    Chief Executive Officer
                                    (Principal Executive Officer)

 /s/ Seth R. Johnson
-----------------------------       Vice President and Chief Financial Officer
Seth R.  Johnson                    and Director (Principal Financial and
                                    Accounting Officer)
             *
-----------------------------       Director
George Foos
             *
-----------------------------       Director
John A. Golden
             *
-----------------------------       Director
John W. Kessler
             *
-----------------------------       Director
Sam N. Shahid, Jr.
             *
-----------------------------       Director
Douglas L. Williams

                                       4
5

     *Seth R. Johnson, by signing his name hereto, signs this document on
behalf of the persons indicated above pursuant to powers of attorney duly
executed by such persons.

                               By /s/ Seth R. Johnson
                                 -------------------------
                                  Seth R. Johnson,
                                  Attorney-in-Fact

                                       5
6

                                 EXHIBIT INDEX

     The following exhibits are filed as part of this Registration Statement:

                                    Exhibit

4.1   Amended and Restated Certificate of Incorporation of the Registrant
      incorporated by reference to Exhibit 3.1 of the Registrant's quarterly
      report on Form 10-Q for the quarter ended November 2, 1996.

4.2   Form of Bylaws of the Registrant incorporated by reference to Exhibit 3.1
      of the Registrant's quarterly report on Form 10-Q for the quarter ended
      November 2, 1996.

5.1   Legal opinion of Vorys, Sater, Seymour and Pease LLP.

15.1  Letter of PricewaterhouseCoopers LLP regarding Unaudited Interim Financial
      Information.

23.1  Consent of PricewaterhouseCoopers LLP.

23.2  Consent of Vorys, Sater, Seymour and Pease LLP (included in the opinion 
      filed as Exhibit 5.1).

24.1  Power of Attorney.

                                       6