My most useful experience with nonprofit organizations comes from serving as president of the Greater Community AIDS Project (Champaign, Ill.) and ART 180 (Richmond, Va.). On the administrative side, it's been helpful to have run a small consulting business organized as a subchapter S corporation.
Both of the above groups were small, young, and overflowing with energy. They also encapsulated two challenges typically faced by nonprofits:
Our treasurer at ART 180 developed an Excel spreadsheet that gave board members the financial information we needed to plan effectively. I'm happy to offer it here for adaptation by other nonprofits: Cashflow Spreadsheet [xls].