While there is no exhaustive directory of nonprofit organizations, there are several directory sites that provide a useful way to find non profit organizations.
The Directory of America’s Charities is a report on charitable organizations which is compiled by US News and World Report. This is a highly recommended resource for finding information about charitable organizations.
Better Business Bureau Wise Giving Alliance – Includes an Accredited Charity Directory
Guidestar provides a database of nonprofit organizations in the US.
Great Nonprofits – a place to find, review, and talk about great—and perhaps not so great—nonprofits.