An S corporation can have no more than 100 shareholders, according to the IRS. Its shareholders must also be allowable owners: generally individuals, certain trusts, and estates, not partnerships, corporations, or nonresident aliens.
An S corporation may have only one class of stock and must be a domestic corporation. To elect S status, the corporation files Form 2553, signed by all of its shareholders.
Source: Internal Revenue Service — S corporations.
Image: Annual shareholders meeting; Krassotkin, CC0, via Wikimedia Commons.