As with so many things the answer is, "it depends." Common practice has adopted the "minimal" rule - keep committees to the minimum number that best meets the board's responsibilities. Having said that, many nonprofit boards of any size require an Executive Committee with well defined authority. It is interesting to note that, with the nearly universal availability of e-mail, current board practice cites less need for an Executive Committee.
The other common committee for nonprofits is the Finance Committee. This committee helps the board carry out its fiduciary responsibilities. As nonprofits grow in size and complexity, boards have been delegating much of the technical oversight to a Finance Committee, which has greater expertise. But the overall financial responsibility remains with the board. It should be noted that the nonprofit accountability requirements have been increasing. Many funding sources now require annual certified audits. A frequently seen guide for moving to annual audits, rather than financial reviews, is when a nonprofit's budget reaches around $350,000.
In response to the nonprofit implications of the American Competitiveness and Corporate Accountability Act of 2002, commonly known as the Sarbanes-Oxley Act, nonprofits are establishing Audit Committees that comply with this law. Some smaller nonprofits develop joint Finance/Audit Committees that then adjourn to reconvene as the Audit Committee. Care must be taken to assure independence of the Audit Committee in this case. Larger nonprofits usually create separate Audit Committees. Many accounting firms offer written guidance for the operations of the Audit Committee. See the Independent Sector explanation of how the Sarbanes-Oxley Act affects nonprofits at http://www.independentsector.org.
The ASU Lodestar Center has identified an additional committee, the Board Development committee, as a growing best practice. This committee replaces the traditional Nominating Committee and is charged with the responsibility of board recruitment, nominating, education and evaluation. Its purpose is to assure the quality of the Board and, thus, assuring the future of the organization.
Other common committees are personnel, resource development, and planning. Having said that, it is true that the more divided up a board becomes the more difficult it is for the board to have informed responsibility for the organization. Therefore. committee formation should be done sparingly and with care.