Not unless your organization is a private foundation. Although nonprofits are required to give their Form 990 "annual information return" to anyone who asks, the Tax Regulations specifically provide that "in the case of a tax--exempt organization other than a private foundation, the term 'annual information return' does not include the name and address of any contributor to the organization." Private foundations are required to disclose the names of donors on Schedule B. The other information about the size and character of the gift must be disclosed.

Since the question was originally published, the IRS has eliminated the requirement to file a Schedule B for all organizations filing Form 990 other than charities (and private foundations that file a Form 990-PF).  (See Nonprofit Issues^®, Vol. XXVIII, No. 3.)  The controversy over disclosure of names of donors continues.