Two classification systems (taxonomies) of not-for-profits
I. IRS Sub-Sections
Here is a list of nonprofits by IRS subsection code that are included in the NTEE classification system, explained further here.
II. NTEE Broad Categories and Major Groups
The National Center for Charitable Statistics web site describes the National Taxonomy of Exempt Entities or NTEE, a classification for nonprofit organizations recognized as tax exempt under the Internal Revenue Code.
Here is an introduction to the concept of NTEE classification, listing the 10 "broad categories" that make up this classification, and the 26 "major groups" that fall within these categories. For a complete manual with in-depth description, examine the NTEE-CC Manual. NOTE: HERE IS AN OLDER VERSION OF THE NTEE-CC MANUAL THAT GIVES BETTER DESCRIPTIONS.
A wealth of statistics can also be found in the Nonprofit Almanac 2016, available by library subscription. Selected data has been updated in the freely available 2019 Nonprofit Sector in Brief almanac.
Domestic
Perhaps the single best directory of U.S. nonprofits on the web, GuideStar (http://www.guidestar.org/) (password access only) offers basic directory information plus financial statements, mission and programs, goals and results, and leaders.
For private foundations specifically, Guidestar can be used, but the The Foundation Directory, available on level A of the library, in Graduate Reference 061 F771d, is also useful.
International
For foreign nonprofits, consult idealist.org. This directory is open access.
Run a Google search on your organization as well, for news about the organization and the organizational home page.
For mention in newspapers, magazine, or trade publication, visit the library subscription database Business Source Complete .
For nonprofits in the Lehigh Valley, visit the library subscription database Morning Call via Proquest.