Here is a summary of non-UC awards and fellowships that graduate students can apply for. This list is not complete. If you know other awards and fellowships, let us know and we will include it in this list.
NSF Graduate Research Fellowship Program (GRFP)
EPA Science To Achieve Results (STAR) Fellowships
Ford Foundation Fellowships
Link Foundation Fellowships
Hertz Foundation Fellowships
Graduate Assistance in Areas of National Need (GAANN) Fellowships
IUPAC Prizes for Young Chemists
Iota Sigma Pi: Anna Louise Hoffman Award
More sources of scholarships and fellowships:
FastWeb
Cornell University Fellowship Database
University of Illinois Fellowship Database
ACS grants and award summary
German Academic Exchange Service (DAAD)