Each agency posts its grant opportunity announcements in at least 2 places:

(1) Its own web site
For an overview of the agencies' missions and funding priorities and links to their lists of funding opportunities,
see: Federal Agency Profiles

and usually

(2) Grants.gov
http://www.grants.gov/

The “Find” feature allows searching for information on competitive grant opportunities from all Federal grant-making agencies from one location. Searches can be done by topic area as well as by agency, date of publication, and other identifying parameters.

Sign up for RSS feed to be notified automatically of future grant opportunities as they are added to the site also can be done.

Grants.gov Overview

In addition, grant announcements and/or general information about the agencies' grant programs may be found at:

Federal Business Opportunities
http://www.fedbizopps.gov/

FedBizOpps is the single government point-of-entry (GPE) for Federal government procurement opportunities over $25,000. Most research opportunities listed in FedBizOpps also are listed at grants.gov. The Dept. of Defense and the Dept. of Energy are the agencies most likely to post opportunity announcements in FedBizOpps.

No registration needed to search funding opportunities

Federal Register
http://www.federalregister.gov/

Published by the Office of the Federal Register, National Archives and Records Administration (NARA), the Federal Register is the official daily publication for rules, proposed rules, and notices of Federal agencies and organizations, as well as executive orders and other presidential documents.

Any notice of funding opportunity that is published in the Federal Register also will be posted in grants.gov. The Dept. of Education (US ED) routinely publishes its grant announcements in the Federal Register in addition to grants.gov.

Catalog of Federal Domestic Assistance
http://www.cfda.gov/

The CFDA provides general descriptions of all Federal programs available to State and local governments (including the District of Columbia); federally-recognized Indian tribal governments; Territories (and possessions) of the United States; domestic public, quasi-public, and private profit and nonprofit organizations and institutions; specialized groups; and individuals.

The database can be searched by a variety of parameters.

The assigned CFDA# identifies the program, but may not be a unique identifier for a specific competition or submission deadline.

Also available at this site are several aids that provide guidance for writing of a proposal to apply for these programs.

Research.gov
http://www.research.gov/

Research.gov improves customer service for the research community by increasing access to information and services while streamlining and standardizing business processes among partner agencies.  Research.gov is also a transparent source for information about federal research spending and outcomes for the general public.

SearchGov.com
http://www.searchgov.com/

This site provides links to virtually all Federal branches, departments, executive agencies, and independent agencies, as well at to State and Local government sites.

Federal agencies & offices that provide  competitively-awarded grants include:

- Centers for Disease Control and Prevention (CDC)
- Corporation for National and Community Service
          (Corp. for Natl. Service) 
- Dept. of Agriculture (USDA)
- Dept. of Commerce (DOC)
- Dept. of Defense (DOD)
- Dept. of Education (US ED)
- Dept. of Energy (DOE)
- Dept. of Health and Human Services (DHHS)
- Dept. of Homeland Security (DHS)
- Dept. of Housing and Urban Development (HUD)
- Dept. of the Interior (DOI)
- Dept. of Justice (DOJ)
- Dept. of Labor (DOL)
- Dept. of State (STATE )
- Dept. of Transportation (DOT)
- Dept. of Veterans Affairs (Veterans Affairs)
- Environmental Protection Agency (EPA)
- Institute for Museum and Library Services (IMLS)
- National Aeronautics and Space Administration (NASA)
- National Archives and Records Administration (NARA)
- National Endowment for the Arts (NEA)
- National Endowment for the Humanities (NEH)
- National Oceanic and Atmospheric Administration (NOAA)
- National Science Foundation (NSF)
- National Transportation Safety Board (NTSB)
- Social Security Administration (SSA)