If you are interested in researching the history of a public or private company, NYPL offers many useful resources to assist you. The history of a public company through mergers, acquisitions, spin-offs or other financial transactions are a matter of public record and not hard to find (at the least, the SEC will have a record). The history of a private company may be more difficult to locate, as the terms are not required to be reported to the Securities and Exchange Commission.
If you are researching an old stock certificate, you can also search by the company's state of incorporation, or their transfer agent (the certificate will list both). Every state in the U.S. has a Division of Corporations, which maintains records for all businesses (public and private) incorporated there. Many states provide an online database of their corporation records, though sometimes only in a certain timeframe, which may not include all of their records on paper. Many of these databases are free to use, but a few states charge a modest fee for an online search.
For older stock certificates, you may want to contact the state's Division of Corporations by phone or e-mail and inquire directly. The state of New York's Corporation & Business Entity database can be found here.
If your stock certificate no longer has value as a traded security, it may nonetheless have value as a collectible. There is a market for old stock certificates as collectibles, for historical interest or aesthetic value as an object. Many collectibles dealers who appraise old stock certificates have websites or advertise online.
Capital Changes Reporter is available in the Business Center's reference collection in the financial services section. A series of spiral-bound records, the Reporter is updated only through 2011, unlike the up-to-date electronic edition.
Hoover's Masterlist of U.S. Companies is available in the Business Center's reference collection, with the call number HF5035.H66