Instead of listing all types of US government grants, it would almost easier to list things for which grants are not available 
I was joking just a bit, but the scope of government grants is huge, so let’s start narrowing it down. First, let us eliminate things that we don’t normally think of as grants, such as food stamps, welfare, foreign aid, the earned income tax credit, and that sort of thing. We can also set aside federal aid to states, even though some of that funding goes into state run grant programs. This thins the list, but it still leaves over 1000 grant programs offered by the 26 Federal grant-making agencies. (see: http://www.grants.gov/TypesofG rants )
Narrowing our search even more, we can leave out everything except Project Grants, which are:
"The funding, for fixed or known periods, of specific projects. Project grants can include fellowships, scholarships, research grants, training grants, traineeships, experimental and demonstration grants, evaluation grants, planning grants, technical assistance grants, survey grants, and construction grants." from: http://12.46.245.173/pls/porta l30/CATALOG.TYP_ASSISTANCE_DYN .show
A listing of the agency grant programs can be found at: http://12.46.245.173/pls/porta l30/!catalog.PROJECT_GRANTS_RP T.show
Each of these programs may have many different components, sub-grants, each with its own eligibility requirements and rules.
So you can see that the scope of government grants is very large. However, looking for specific grants has been made easier with one web site acting as the government grant information hub. Start at: http://www.grants.gov/Index
Good luck and good grants.
