The National Academies Office has two websites where opportunities can be found. Research Associate Awards for Postdoctoral and Senior Associates or the Fellowship Office
NSF has opportunities offered through their IGERT: Integrative Graduate Education and Research Traineeship Program
The American Association for the Advancement of Science, in partnership with NIH offers a postdoctoral fellowship on the integration of science on government policy making.
NIH also offers predoctoral research training opportunities.
State University of New York/Downstate Medical Center lists many funding opportunities for PostDocs. While the deadlines for applications are mostly out of date the links are still valid.
ScienceNet, The Center for Science Education at Emory College, offers a variety of links for graduates and beyond. There is information on fellowship opportunities as well as career information.
UC Berkeley School of Engineering has links and contact information on various Graduate Engineering Fellowships.
PhDs.org is a website dedicated to science, math and engineering students. Information is offered for prospective and current PhD students to help with grad school choices, funding and career planning.