Examples
The largest nonprofit organization in the United States (and the world) is the Bill and Melinda Gates Foundation, which has an endowment of approximately $60 billion ($27 billion from the Gateses and $30 billion from Warren Buffett in Spring 2006). The second largest is the Howard Hughes Medical Institute, which has an endowment of approximately $14.8 billion. Elsewhere in the world, the largest nonprofit organization is probably the British Wellcome Trust, which is a "charity" in British usage. Note that this assessment excludes universities, at least a few of which have assets in the tens of billions of dollars.
Of course measuring a nonprofit by its monetary size has obvious limitations, as the power and significance of nonprofits are defined by more qualitative measurements such as effectiveness at carrying out charitable mission and goals.
Some nonprofits which are particularly well known, often for the charitable or social nature of their activities conducted over a long period of time, include Amnesty International, the Better Business Bureau, Oxfam, Carnegie Corporation of New York, DEMIRA Deutsche Minenraeumer e.V. - German Mine Clearer, Goodwill Industries, the Red Cross and Red Crescent organizations, UNESCO, IEEE, WWF and SOS Children's Villages.
However, there are also millions of smaller nonprofit organizations that provide social services or the arts to people throughout the world. There are more than 1.6 million nonprofits in the United States alone. For more see Wikipedia articles on non-profit organizations