The just-released Statistics of Income Bulletin (Fall 2004) includes Charities and Other Tax-Exempt Organizations, 2001 by Paul Arnsberger (SOI).  Here is the summary:

Nonprofit charitable organizations held over $1.6 trillion in assets and filed over 240,000 information returns for Tax Year 2001.

For related data, see here.  For other exempt organization tax data, see here.