<PAGE>   1
                                                                   EXHIBIT 10.13


            STOCKHOLDERS AGREEMENT, dated as of May 1, 1991, among ROGER KING,
an individual residing at 1301 Spanish River Road, Boca Raton, Florida 33432,
MICHAEL KING, an individual residing at 28026 Sea Lane, Malibu, California
90265, RICHARD KING, an individual residing at 21 Compass Island, Fort
Lauderdale, Florida 33308 and DIANA KING, an individual residing at Lee's Hill
Road, New Vernon, New Jersey 07920 (said individuals, together with any
transferees thereof who execute and deliver the agreement required by Section 
3(d) hereof and any executor, administrator or personal representative of any of
the foregoing, being sometimes hereinafter referred to individually as a
"Stockholder" and, collectively, as the "Stockholders") and KING WORLD
PRODUCTIONS, INC., a Delaware corporation (the "Company").

            WHEREAS, the Stockholders and the Company, together with certain
other individuals no longer stockholders of record of the Company, were parties
to that certain Stockholders Agreement, dated as of October 25, 1984 (the
"Original Stockholders Agreement"), pursuant to which restrictions were placed
on the resale by the individual parties of shares of Common Stock, $.01 par
value, of the Company ("Common Stock") held by them; and

            WHEREAS, the Company and the individual parties to such agreement
who remain stockholders of record of the Company desire to terminate the
Original Stockholders Agreement; and

            WHEREAS, each of the Stockholders owns such number of shares of
Common Stock, and such number of shares of Common Stock subject to an option to
purchase ("Option Shares"), as is set forth opposite his or her respective name
under the appropriate caption on Schedule I hereto; and

            WHEREAS, the Company and the Stockholders believe that it is in the
best interests of the Company and the Stockholders that provision be made for
the orderly disposition of shares of Common Stock that individual Stockholders
may wish to sell in the public securities markets, while preserving the ability
of each Stockholder to make independent decisions regarding the amount and
timing of any such sales; and for the grant to the Company of a right of first
refusal to purchase any shares of Common Stock that individual Stockholders may
wish to sell;

            NOW, THEREFORE, in consideration of the mutual covenants herein
contained, the parties hereby agree as follows:

            SECTION 1. Restrictions on Transfer of Common Stock. The
Stockholders severally agree with each other and with the Company that they will
not, so long as this Agreement is in effect, directly or indirectly sell,
pledge, give, bequeath,
<PAGE>   2
transfer, assign, or in any other way whatsoever encumber or dispose of
(hereinafter collectively called "transfer") any of the shares of Common Stock,
or any interest therein, or any stock certificate or certificates representing
the same, or any voting trust certificate or certificates issued in respect of
any such shares, now or hereafter at any time owned by them, in violation of the
restrictions imposed by this Agreement. The term "Common Stock" as used in this
Agreement shall include Common Stock certificates, scrip representing fractional
shares of Common Stock, Vested Option Shares (as hereinafter defined) and
presently exercisable warrants or other presently exercisable rights to purchase
Common Stock, and Common Stock received by way of dividend or upon an increase,
reduction, substitution or reclassification of stock of the Company or upon any
merger, consolidation or reorganization of the Company. References to numbers of
shares of Common Stock, as constituted on the date hereof, shall be
automatically adjusted to take into account any such dividend, increase,
reduction, substitution, reclassification, merger, consolidation or
reorganization.

            SECTION 2. Limit on Sales by Stockholders. (a) Each of the
Stockholders agrees that in the 1991 calendar year, including that portion of
the 1991 calendar year preceding the date hereof, he or she will not sell in
transactions effected on national or foreign securities exchanges or in the
over-the-counter market (hereinafter referred to as "Public Sales"), more than
the greater of (i) 1% of the number of shares of Common Stock outstanding on the
date of the Agreement, and (ii) the average weekly reported volume of trading in
the Common Stock on the New York Stock Exchange during the four calendar week
period ending on May 3, 1991.

            (b) Each of the Stockholders agrees that subsequent to the 1991
calendar year, he or she will not sell in Public Sales (i) in any calendar year,
more than the greater of (x) 200,000 shares and (y) 10% of his or her aggregate
holdings of Common Stock as of January 1 of such year (including, for the
purpose of calculating such aggregate holdings, any Option Shares subject to an
option that is exercisable as of such date ("Vested Option Shares")) and (ii) in
any consecutive three month period, more than 250,000 shares of Common Stock.

            (c) Notwithstanding the foregoing, the executor or administrator of
the estate of a Stockholder or a trustee of a trust includible in the gross
estate of a deceased Stockholder for federal estate or state inheritance tax
purposes may sell a number of shares of Common Stock not to exceed the aggregate
amount of the federal estate and state inheritance taxes payable on account of
the death of such Stockholder.

            SECTION 3. Right of First Refusal. (a) Subject to the limitations of
Section 2 hereof, any Stockholder (a "Selling
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Stockholder") who wishes to sell any shares of Common Stock shall promptly
deliver to the Company a notice of intention to sell (a "Notice of Intention to
Sell") setting forth the securities to be sold ("Subject Shares"), the proposed
date of sale and, if the proposed sale is not by way of Public Sale, the
proposed purchase price and terms of sale, which shall be for cash or
obligations to pay cash. In the case of a proposed sale other than a Public
Sale, upon receipt of the Notice of Intention to Sell the Company shall have the
right to elect to purchase all (but not less than all) of the Subject Shares at
the Offering Price (as hereinafter defined), and upon such other terms and
conditions as are stated in the Notice of Intention to Sell. In the case of a
proposed Public Sale, upon receipt of the Notice of Intention to Sell the
Company shall have the right to elect to purchase all or any portion of the
Subject Shares at the Offering Price. The Company's election hereunder shall be
made (if at all) by notice in accordance with Section 6 hereof (a "Notice of
Election") to the Selling Stockholder within five (5) business days after
receipt by the Company of the Notice of Intention to Sell (the "Acceptance
Period"). For the purpose of this paragraph 3(a), "Offering Price" shall mean
(i) in the case of a sale other than by way of a Public Sale, the price stated
in the Notice of Intention to Sell, and (ii) in the case of a Public Sale, the
highest closing price of the Common Stock on any national securities exchange on
which the Common Stock is listed on the day on which the Notice of Intention to
Sell is given to the Company (or, if such day is not a trading day, on the
trading day preceding such day), or, if the Common Stock is no longer listed on
any national securities exchange, the closing price (or, in the absence of a
closing price, the closing bid price) for the Common Stock in the
over-the-counter market on such day.

            (b) If an effective acceptance is timely received with respect to
all the Subject Shares, then the Selling Stockholder shall sell the Subject
Shares to the Company at the Offering Price and upon the other terms specified
in the Notice of Intention to Sell. If an effective acceptance shall not be
received in respect of all the Subject Shares, then the Selling Stockholder (i)
if the proposed sale is other than a Public Sale, may sell the Subject Shares to
its proposed buyer(s) at a price not less than the Offering Price and on other
terms and conditions not more favorable to such buyer(s) than those stated in
the Notice of Intention to Sell, or (ii) if the proposed sale is a Public Sale,
shall sell to the Company at the Offering Price the number of Subject Shares
specified in the Notice of Election, in either case as soon as practicable
following the receipt of the Notice of Election. Any Subject Shares which the
Company shall not have elected to purchase in a timely Notice of Election may be
sold by the Selling Stockholder in accordance with the method and upon the terms
and conditions specified in the Notice of Intention to Sell, provided, however,
that any Subject Shares that are not sold within ninety (90) days following the
end of
<PAGE>   4
the Acceptance Period shall once again become subject to the provisions of this
Section 3.

            (c) No sale of Common Stock may be effected by a Stockholder except
in accordance with paragraphs (a) and (b) of this Section 3. No transfer of
Common Stock other than by way of sale may be effected by a Stockholder unless
and until the transferee shall have executed and delivered to the Company and to
each other Stockholder a written instrument whereby such transferee becomes a
party to this Agreement, and agrees to comply with all of the terms and
conditions of this Agreement with respect to all shares of Common Stock at any
time owned by such transferee; provided, however, that any Stockholder may
transfer by gift up to 200,000 shares of Common Stock in any consecutive
twelve-month period free of the provisions of this sentence.

            (d) No transfer of Common Stock may be effected by a Stockholder,
unless and until the transferring Stockholder shall have furnished to the
Company, if requested, an opinion of counsel reasonably satisfactory to the
Company to the effect that the proposed transfer may be effected without
registration under the Securities Act of 1933, as amended.

            SECTION 4. Legend on Stock Certificates. Each certificate
representing shares of Common Stock held by any Stockholder shall bear the
following legend until such time as the shares represented thereby are no longer
subject to the provisions hereof:

            THE SHARES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO THE TERMS
            AND CONDITIONS OF A STOCKHOLDERS AGREEMENT, DATED AS OF MAY 1, 1991,
            AMONG KING WORLD PRODUCTIONS, INC. (THE "CORPORATION") AND CERTAIN
            HOLDERS OF SHARES OF THE OUTSTANDING CAPITAL STOCK OF THE
            CORPORATION. COPIES OF SUCH AGREEMENT MAY BE OBTAINED AT NO COST BY
            WRITTEN REQUEST MADE BY THE HOLDER OF RECORD OF THIS CERTIFICATE TO
            THE CORPORATION.

            SECTION 5. Duration of Agreement. The rights and obligations of the
parties under this Agreement shall terminate as to each Stockholder upon the
earlier to occur of (i) the date on which the aggregate ownership of shares of
Common Stock of such Stockholder is reduced below 200,000 shares (including
Vested Option Shares) and (ii) the date on which the Common Stock ceases to be
listed on a national securities exchange or quoted on the NASDAQ automated
quotation system.

            SECTION 6. Representations and Warranties. Each Stockholder
represents and warrants, severally and not jointly, to the Company and to the
other Stockholders as follows:
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            (a) The execution, delivery and performance of this Agreement by
such Stockholder will not violate any provision of law, any order of any court
or other agency of government, or any provision of any indenture, agreement or
other instrument to which such Stockholder or any of his or her properties or
assets is bound, or conflict with, result in a breach of or constitute (with due
notice or lapse of time or both) a default under any such indenture, agreement
or other instrument, or result in the creation or imposition of any lien, charge
or encumbrance of any nature whatsoever upon any of the properties or assets of
such Stockholder.

            (b) This Agreement has been duly executed and delivered by such
Stockholder and constitutes the legal, valid and binding obligation of such
Stockholder, enforceable in accordance with its terms.

            (c) As of the date hereof, the shares of Common Stock listed on
Schedule I hereto opposite the name of such Stockholder constitute all the
shares of Common Stock of the Company owned by such Stockholder, and the Option
Shares listed on Schedule I hereto opposite the name of such Stockholder
constitute all the shares of Common Stock which such Stockholder has a right to
acquire; such shares of Common Stock are owned by such Stockholder free and
clear of any security interest, pledge, lien, claim, encumbrance or interest
whatsoever and may be voted by such Stockholder at his or her discretion without
hindrance of any person, and such Stockholder does not have any right or
obligation to acquire any additional shares of the capital stock of the Company.

            SECTION 7. Notices. Except as otherwise expressly provided herein,
any and all notices, designations, consents, offers, acceptances or other
communications provided for herein shall be given (i) in writing transmitted by
telecopier, delivered personally or sent by a nationally recognized overnight
courier service, or (ii) orally in person or by telephone, with written
confirmation by one of the means described in (i) above, in either case, if to
the Company, at:

                  1700 Broadway
                  New York, New York 10019
                  Attention: Chief Operating Officer
                  (telecopier number: (212) 247-7674)
or
                  830 Morris Turnpike
                  Short Hills, New Jersey 07078
                  Attention:  Controller
                  (telecopier number: (201) 376-7787)

<PAGE>   6
or, if to any Stockholder, at

Roger King:       1301 Spanish River Road
                  Boca Raton, Florida 33432

Michael King:     3200 Retreat Court
                  Malibu, California 90265

Richard King:     21 Compass Island
                  Fort Lauderdale, Florida 33308

Diana King:       Lee's Hill Road
                  New Vernon, New Jersey 07920

Notice shall be deemed given, for all purposes, when received.

            SECTION 8. Benefits of Agreement. This Agreement shall be binding
upon and enure to the benefit of the parties hereto and their respective
successors and permitted transferees.

            SECTION 9. Amendment of Agreement. This Agreement may be amended,
modified or revoked in whole or in part, but only by a written instrument that
specifically refers to this Agreement and expressly states that it constitutes
an amendment, modification or revocation hereof, as the case may be, and only if
such written instrument has been signed by each of the Stockholders and the
Company.

            SECTION 10. Interpretation of Agreement. The provisions of this
Agreement shall be applied and interpreted in a manner consistent with each
other so as to carry out the purposes and intent of the parties hereto, but if
for any reason any provision hereof is determined to be unenforceable or
invalid, such provision or such part thereof as may be unenforceable or invalid
shall be deemed severed from this Agreement and the remaining provisions carried
out with the same force and effect as if the severed provision or part thereof
had not been a part of this Agreement.

            SECTION 11. Counterparts. This Agreement may be executed in one or
more counterparts, each of which shall be deemed to be an original, but all of
which taken together shall constitute one and the same instrument.

            SECTION 12. Entire Agreement. This Agreement constitutes the entire
agreement of the parties with respect to the subject matter hereof, and
supersedes the Original Stockholders Agreement, which is hereby terminated, and
all other previous agreements with respect to the subject matter hereof.
<PAGE>   7
            IN WITNESS WHEREOF, the parties hereto have duly executed and
delivered this Stockholders Agreement as of the date first above written.

                                    KING WORLD PRODUCTIONS, INC.


                                    By /s/ Stephen W. Palley
                                      ------------------------------------------
                                          Executive Vice President
[Corporate Seal]

Attest:


------------------------
     Secretary



                                       /s/ Roger King
                                    --------------------------------------------
                                                 Roger King


                                       /s/ Michael King
                                    --------------------------------------------
                                                 Michael King


                                       /s/ Richard King
                                    --------------------------------------------
                                                 Richard King


                                       /s/ Diana King
                                    --------------------------------------------
                                                 Diana King
<PAGE>   8
                                      Schedule I


<TABLE>
<CAPTION>
  Name of              Common          Option
Stockholder             Stock          Shares
-----------           ---------      ---------
<S>                   <C>            <C>
Roger King            3,122,259      1,200,000

Michael King          3,347,259      1,200,000

Richard King          3,131,506             --

Diana King            3,147,259             --
</TABLE>