Grants are generally aimed at basic research and applied research. Unlike contract research and development, grants do not allow profit to be part of the budget. That said, they can still be a great source of funding for research.
The main place to look for grants is Grants.Gov. This web site provides a common place for all government agencies to post grants. The mission of grants.gov is to:
Provide a common website for federal agencies to post discretionary funding opportunities and for grantees to find and apply to them.
There are a wide range of grants listed here from a number of agencies. Most grants are listed here, though some BAAs will also provide grant option to a contract and in these cases the grant may not appear in grants.gov.