When thinking about the composition of a charity's board of directors, a common rule of thumb is that 1/3 of the board should be people who have money and generously contribute to the organization. Another third should be people who might not have a lot of money themselves, but are good at asking for contributions from other people. The rest of the board should be people who may not have money or know people with it, but who have the energy it takes to get things done in an organization.
According to Philanthropy Today, three board members of New York's Museum of Modern Art (commonly known by it's stylish acronym, MOMA) are billionaires. I think it's safe to say that MOMA does not have any funding problems. Yay for art.