International Institute for Education. Offers a number of fellowships for students and non-students. Most notable include Fulbright Fellowships (which are often open to non-students), National Security Education Program for Undergraduates and Graduates (study abroad program), and many others. They also maintain a wonderful site on Scholarships for US and International Students.
Social Science Research Council SSRC fellowship and grant programs provide support and professional recognition to innovators within fields, and especially to younger researchers whose work and ideas will have longer-term impact on society and scholarship.
American Council of Learned Societies. CLS offers fellowships and grants in over one dozen programs, for research in the humanities and humanistic social sciences at the doctoral and postdoctoral levels.
AMIDEAST. Administers a number of private, institutional, and non-U.S. government scholarship programs for students and professionals from the Middle East and North Africa, most of which are for study at U.S. universities.