Grants.gov: Provides a search engine for federal opportunities with instructions at the site.
Department of Agriculture: Provides a general overview of the agency. For national competitions go to the National Research Initiative Competitive Grant Program.
Department of Energy: Offers various funding opportunities in the fields of basic energy sciences, high energy physics, nuclear physics, advanced scientific computing research, fusion energy sciences, biological and environmental research, and planning and analysis.
Department of Education: Offers funding opportunities to improve education and educational systems in the United States. Deadlines vary.
Environmental Protection Agency: Provides research and program funding related to protection of human health and the environment. For specifics of funding, visit Contracts, Grants and Financing section of the EPA website.
NASA: Supports grant and fellowship programs related to space exploration, scientific discovery, and aeronautics research.
National Endowment for the Arts: Provides grants for the arts and art education.
National Endowment for the Humanities: Provides support to scholars and organizations for research and projects/programs related to the humanities.
National Institutes of Health: Offers fellowship and funding opportunities for a wide range of medical and behavioral research.
National Science Foundation: Funds research and education in most fields of science, engineering, and the social sciences. Deadlines vary. Visit these pages for specifics:
Office of Naval Research: Provides grants to universities and private foundations for research that will enhance the technology of the United States Navy and Marine Corps.
Federal Register: Search the Federal Register for official announcements of new programs, regulations, and changes to programs/regulations etc.