<PAGE>   1
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MARCH 20, 2000

                                                           REGISTRATION NO. 333-
--------------------------------------------------------------------------------
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                               ------------------
                              THE HERTZ CORPORATION
             (Exact Name of Registrant as Specified in Its Charter)
<TABLE>
<S>                                                             <C>
               DELAWARE                                                      13-1938568
(State or Other Jurisdiction of Incorporation                   (I.R.S. Employer Identification No.)
or Organization)

        225 BRAE BOULEVARD
PARK RIDGE, NEW JERSEY 07656-0713
(Address and Zip Code of Principal Executive Offices)
</TABLE>


                              THE HERTZ CORPORATION
                       LONG-TERM EQUITY COMPENSATION PLAN
                            (Full Title of the Plan)

                              HAROLD E. ROLFE, ESQ.
              SENIOR VICE PRESIDENT, GENERAL COUNSEL AND SECRETARY
                               225 BRAE BOULEVARD
                        PARK RIDGE, NEW JERSEY 07656-0713
                     (Name and Address of Agent For Service)

                                  201-307-2000
          (Telephone Number, Including Area Code, of Agent For Service)

<TABLE>
<CAPTION>
======================================================================================================
                                  CALCULATION OF REGISTRATION FEE
======================================================================================================
                                            Proposed Maximum    Proposed Maximum
  Title of Securities       Amount To Be   Offering Price Per      Aggregate            Amount of
   To Be Registered          Registered        Share (1)        Offering Price (2)  Registration Fee
------------------------- ---------------- ------------------- ------------------- -------------------
<S>                        <C>            <C>                   <C>                 <C>
  Class A Common Stock
     $.01 par value           2,650,000
       per share               Shares          $39.67            $105,125,500           $27,753
======================================================================================================
</TABLE>

(1) Based on the market price of the Class A Common Stock of the registrant at
    which employee stock options have been granted and the market price of the
    Class A Common Stock of the registrant on March 15, 2000 computed in
    accordance with Rule 457(c) and (h) under the Securities Act of 1933.

(2) This amount is the sum of (a) the aggregate option price of 2,630,740 shares
of Class A Common Stock of the registrant subject to options granted under the
Long-Term Equity Compensation Plan of the registrant and outstanding on March
15, 2000, with a weighted average option price of $39.75, and (b) the assumed
aggregate option price of the 19,260 remaining shares of Class A Common Stock
being registered, based on the market price of Class A Common Stock of the
registrant on March 15, 2000, in accordance with Rule 457(c) and (h) under the
Securities Act of 1933.

In addition, pursuant to Rule 416(c) under the Securities Act of 1933, this
registration statement also covers an indeterminate amount of interests to be
offered or sold pursuant to the employee benefit plan described herein.

                                Page 1 of 8 pages

                         The Exhibit Index is on page 5


<PAGE>   2




                           INFORMATION REQUIRED IN THE
                             REGISTRATION STATEMENT

INCORPORATION OF CONTENTS OF PRIOR REGISTRATION STATEMENTS

        The contents of Registration Statement No. 333-32543 are incorporated
herein by reference.

ITEM 8. EXHIBITS.

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                       DESCRIPTION
------                       -----------
<S>            <C>
 4(a)          Form of The Hertz Corporation Long-Term Equity Compensation Plan,
               Amended and Restated as of August 25, 1997, filed as Exhibit 4(a)
               to the registrant's Amendment No. 1 to Form S-8 on August 28,
               1997 and incorporated herein by reference.

*5             Opinion of Harold E. Rolfe, Senior Vice President, General
               Counsel and Secretary of The Hertz Corporation, with respect to
               the legality of the securities being registered hereunder.

*23            Consent of PricewaterhouseCoopers LLP.

*24            Powers of Attorney.
</TABLE>

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

*Filed with this Registration Statement

                                Page 2 of 8 pages

<PAGE>   3


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 Borough of Park Ridge, State of New Jersey, on this 20th day
of March, 2000.

                                     THE HERTZ CORPORATION

                                     By:      /s/ PAUL J. SIRACUSA
                                        ----------------------------------
                                     Paul J. Siracusa
                                     Title:  Executive Vice President and
                                             Chief Financial 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.

<TABLE>
<CAPTION>
SIGNATURE                          TITLE(S)                       DATE
---------                          --------                       ----
<S>                              <C>                             <C>
    /s/  CRAIG R. KOCH             President and Chief
---------------------------        Executive Officer
         (Craig R. Koch)           (Principal Executive Officer)  March 20, 2000

    /s/  PAUL J.SIRACUSA           Executive Vice President and
---------------------------        Chief Financial Officer
       (Paul J. Siracusa)          (Principal Financial Officer)  March 20, 2000

    /s/  RICHARD J. FOTI           Controller
---------------------------        (Principal Accounting
       (Richard J. Foti)           (Officer)                       March 20, 2000

    /s/  FRANK A.OLSON
---------------------------
        (Frank A. Olson)           Chairman of the Board          March 20, 2000

              *
---------------------------
        (W. Wayne Booker)          Director                       March 20, 2000

              *
---------------------------
       (Louis C. Burnett)          Director                       March 20, 2000

              *
---------------------------
      (Michael T.Monahan)          Director                       March 20, 2000
</TABLE>

                                Page 3 of 8 pages
<PAGE>   4

<TABLE>
<S>          <C>                  <C>                            <C>
             *
--------------------------
      (Peter J. Pestillo)          Director                       March 20, 2000

             *
--------------------------
      (John M. Rintamaki)          Director                       March 20, 2000

             *
--------------------------
      (John M. Thompson)           Director                       March 20, 2000

             *
--------------------------
      (Joseph A. Walker)           Director                       March 20, 2000
</TABLE>

*By signing his name hereto, Paul J. Siracusa signs this document on behalf of
 each of the persons indicated above pursuant to powers of attorney duly
 executed by such persons.

By:     /s/ PAUL J. SIRACUSA
   ----------------------------
       (Attorney-in-Fact)

                                Page 4 of 8 pages

<PAGE>   5


                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                           DESCRIPTION
------                           -----------
<S>            <C>
4(a)              Form of The Hertz Corporation Long-Term Equity Compensation
                  Plan, Amended and Restated as of August 25, 1997, filed as
                  Exhibit 4(a) to the registrant's Amendment No. 1 to Form S-8
                  on August 28, 1997.

*5                Opinion of Harold E. Rolfe, Senior Vice President, General
                  Counsel and Secretary of The Hertz Corporation, with respect
                  to the legality of the securities being registered hereunder.

*23               Consent of PricewaterhouseCoopers LLP.

*24               Powers of Attorney.
</TABLE>

*Filed herewith.

                                Page 5 of 8 pages
[{"type": "S-8", "sequence": "1", "description": "THE HERTZ CORPORATION", "secsgml_size_bytes": 9382}]
{"company-data": {"conformed-name": "HERTZ CORP", "cik": "0000047129", "assigned-sic": "7510", "irs-number": "131938568", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-32868", "film-number": "574201"}, "business-address": {"street1": "225 BRAE BLVD", "city": "PARK RIDGE", "state": "NJ", "zip": "07656", "phone": "2013072000"}, "mail-address": {"street1": "225 BRAE BLVD", "city": "PARK RIDGE", "state": "NJ", "zip": "07656"}}
1
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MARCH 20, 2000

                                                           REGISTRATION NO. 333-
--------------------------------------------------------------------------------
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                               ------------------
                              THE HERTZ CORPORATION
             (Exact Name of Registrant as Specified in Its Charter)
DELAWARE                                                      13-1938568
(State or Other Jurisdiction of Incorporation                   (I.R.S. Employer Identification No.)
or Organization)

        225 BRAE BOULEVARD
PARK RIDGE, NEW JERSEY 07656-0713
(Address and Zip Code of Principal Executive Offices)
THE HERTZ CORPORATION
                       LONG-TERM EQUITY COMPENSATION PLAN
                            (Full Title of the Plan)

                              HAROLD E. ROLFE, ESQ.
              SENIOR VICE PRESIDENT, GENERAL COUNSEL AND SECRETARY
                               225 BRAE BOULEVARD
                        PARK RIDGE, NEW JERSEY 07656-0713
                     (Name and Address of Agent For Service)

                                  201-307-2000
          (Telephone Number, Including Area Code, of Agent For Service)
======================================================================================================
                                  CALCULATION OF REGISTRATION FEE
======================================================================================================
                                            Proposed Maximum    Proposed Maximum
  Title of Securities       Amount To Be   Offering Price Per      Aggregate            Amount of
   To Be Registered          Registered        Share (1)        Offering Price (2)  Registration Fee
------------------------- ---------------- ------------------- ------------------- -------------------
Class A Common Stock
     $.01 par value           2,650,000
       per share               Shares          $39.67            $105,125,500           $27,753
======================================================================================================
(1) Based on the market price of the Class A Common Stock of the registrant at
    which employee stock options have been granted and the market price of the
    Class A Common Stock of the registrant on March 15, 2000 computed in
    accordance with Rule 457(c) and (h) under the Securities Act of 1933.

(2) This amount is the sum of (a) the aggregate option price of 2,630,740 shares
of Class A Common Stock of the registrant subject to options granted under the
Long-Term Equity Compensation Plan of the registrant and outstanding on March
15, 2000, with a weighted average option price of $39.75, and (b) the assumed
aggregate option price of the 19,260 remaining shares of Class A Common Stock
being registered, based on the market price of Class A Common Stock of the
registrant on March 15, 2000, in accordance with Rule 457(c) and (h) under the
Securities Act of 1933.

In addition, pursuant to Rule 416(c) under the Securities Act of 1933, this
registration statement also covers an indeterminate amount of interests to be
offered or sold pursuant to the employee benefit plan described herein.

                                Page 1 of 8 pages

                         The Exhibit Index is on page 5
2

                           INFORMATION REQUIRED IN THE
                             REGISTRATION STATEMENT

INCORPORATION OF CONTENTS OF PRIOR REGISTRATION STATEMENTS

        The contents of Registration Statement No. 333-32543 are incorporated
herein by reference.

ITEM 8. EXHIBITS.
EXHIBIT
NUMBER                       DESCRIPTION
------                       -----------
4(a)          Form of The Hertz Corporation Long-Term Equity Compensation Plan,
               Amended and Restated as of August 25, 1997, filed as Exhibit 4(a)
               to the registrant's Amendment No. 1 to Form S-8 on August 28,
               1997 and incorporated herein by reference.

*5             Opinion of Harold E. Rolfe, Senior Vice President, General
               Counsel and Secretary of The Hertz Corporation, with respect to
               the legality of the securities being registered hereunder.

*23            Consent of PricewaterhouseCoopers LLP.

*24            Powers of Attorney.
-----------------------------------------------

*Filed with this Registration Statement

                                Page 2 of 8 pages
3

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 Borough of Park Ridge, State of New Jersey, on this 20th day
of March, 2000.

                                     THE HERTZ CORPORATION

                                     By:      /s/ PAUL J. SIRACUSA
                                        ----------------------------------
                                     Paul J. Siracusa
                                     Title:  Executive Vice President and
                                             Chief Financial 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.
SIGNATURE                          TITLE(S)                       DATE
---------                          --------                       ----
/s/  CRAIG R. KOCH             President and Chief
---------------------------        Executive Officer
         (Craig R. Koch)           (Principal Executive Officer)  March 20, 2000

    /s/  PAUL J.SIRACUSA           Executive Vice President and
---------------------------        Chief Financial Officer
       (Paul J. Siracusa)          (Principal Financial Officer)  March 20, 2000

    /s/  RICHARD J. FOTI           Controller
---------------------------        (Principal Accounting
       (Richard J. Foti)           (Officer)                       March 20, 2000

    /s/  FRANK A.OLSON
---------------------------
        (Frank A. Olson)           Chairman of the Board          March 20, 2000

              *
---------------------------
        (W. Wayne Booker)          Director                       March 20, 2000

              *
---------------------------
       (Louis C. Burnett)          Director                       March 20, 2000

              *
---------------------------
      (Michael T.Monahan)          Director                       March 20, 2000
Page 3 of 8 pages
4
*
--------------------------
      (Peter J. Pestillo)          Director                       March 20, 2000

             *
--------------------------
      (John M. Rintamaki)          Director                       March 20, 2000

             *
--------------------------
      (John M. Thompson)           Director                       March 20, 2000

             *
--------------------------
      (Joseph A. Walker)           Director                       March 20, 2000
*By signing his name hereto, Paul J. Siracusa signs this document on behalf of
 each of the persons indicated above pursuant to powers of attorney duly
 executed by such persons.

By:     /s/ PAUL J. SIRACUSA
   ----------------------------
       (Attorney-in-Fact)

                                Page 4 of 8 pages
5

                                  EXHIBIT INDEX
EXHIBIT
NUMBER                           DESCRIPTION
------                           -----------
4(a)              Form of The Hertz Corporation Long-Term Equity Compensation
                  Plan, Amended and Restated as of August 25, 1997, filed as
                  Exhibit 4(a) to the registrant's Amendment No. 1 to Form S-8
                  on August 28, 1997.

*5                Opinion of Harold E. Rolfe, Senior Vice President, General
                  Counsel and Secretary of The Hertz Corporation, with respect
                  to the legality of the securities being registered hereunder.

*23               Consent of PricewaterhouseCoopers LLP.

*24               Powers of Attorney.
*Filed herewith.

                                Page 5 of 8 pages