Some states, such as California and Texas, have special provisions allowing you to create what is known as a "statutory close corporation." Close corporations generally are formed in the same way as ordinary corporations, but the articles of incorporation for a close corporation must state that the corporation shall be considered a "close corporation" and impose restrictions on transfer of shares of stock. Close corporations also must have a limited number of shareholders -- often 35 or 50 shareholders maximum. For state-specific requirements on forming a close corporation, see the state pages on forming a corporation.
The major reason for forming a close corporation is that it allows shareholders to operate the business under the terms of a shareholders' agreement, which can provide for greater flexibility and informality in managing the affairs of the business (as compared to an ordinary corporation). Shareholders of a close corporation may agree to waive certain operating formalities, such as required shareholder or board meetings. Pursuant to the terms of such an agreement, they can also dispense with the need to form a board of directors and name corporate officers, and they (the shareholders) may run the corporation themselves in a de-centralized fashion. (Incidentally, they may also agree to a distribution of corporate profits other than proportionally based on share ownership.) The downside is that a shareholders' agreement that allows shareholders to manage the corporation may make the shareholders liable for acts or omissions for which the corporate directors are usually liable.
Operating as a close corporation is not popular among incorporators. Negotiating and drafting an effective shareholders' agreement may be a complex and costly undertaking, and there is no apparent advantage of operating as a close corporation rather than an LLC (which also features decentralized management and limited liabiliy and no double taxation). If you are interested in forming a close corporation, you should consult with a lawyer.