Because of the massive size of this list, it has been split into two lists. It is worth perusing both for good graphics. The introductory text is identical.
Unsurprisingly, the Library of Congress has the best explanation of what can, and cannot, be used in terms of imagery created by other people.
One item most people do not realize is that, per information from the U.S. Copyright Office, “Works by the U.S. Government are not eligible for U.S. copyright protection.” (Circular 1 [pdf], “Copyright Basics,” page 5.) Please note that those agencies may, however, use images created by others who retain copyright. This happens particularly often with the Smithsonian Institutes, but also with other agencies when employees submit images they took documenting their work.
In my experience, online images in government agency archives clearly state whether the copyright has any restrictions or not. Most agencies have Flickr and / or Instagram accounts. I included these, but please note that much more care must be used when perusing these accounts for images. They are far more likely to have restrictions than the ones on the main departmental websites. However, several agencies have switched from official pages on their websites to official Flickr pages, so it is still worth checking.
If an image has copyright restrictions, restrictions will normally be clearly stated including what they are and who to contact, if known (and it usually is). They also provide a clear byline for providing attribution. Even when attribution is not legally required, such as in pre-1922 images, it is courteous to note the source, even if it is little more than “Library of Congress”.
The biggest downside can be, as in the case of Library of Congress, difficulty in searching through all the results to find an image that suits. It is not at all unusual to have over 1000 results, most of them in black and white. I just learned that the best way to narrow the search to only items in color is to include the word “color” in the search. (Yes, it really is that simple.)
Agencies
Bureau of Indian Affairs (Flickr)
Department of Agriculture (USDA) (Flickr)
Department of Commerce (Flickr)
Department of Education (Flickr)
Department of Health and Human Services (Flickr)
Department of Housing and Urban Development (HUD) (Flickr)
Department of the Treasury (Flickr)
US Mint (no Flickr) – Historical
Department of Defense (Flickr)
Army Corps of Engineers (Flickr)
Coast Guard (Flickr) – Historical Images
National Guard (Flickr)
Veterans Affairs (VA) (Flickr)
Emergency Services
Federal Emergency Management Agency (FEMA) (no Flickr)
Interagency Fire Administration (Picasa)
Executive Branch and Legislature
The House of Representatives (no Flickr) – Historical Images
National Archives (Flickr, Instagram)
The Senate (no Flickr) (Republicans) (Democrats) (Senate Artwork)
Law Enforcement and Justice
Bureau of Indian Affairs Community Policing (no Flickr)
Bureau of Alcohol, Tobacco, Firearms, and Explosives (no Flickr)
Central Intelligence Agency (CIA) (Flickr)
Department of Homeland Security (DHS) (Flickr)
Department of Justice (Office of Public Affairs) (Instagram)
Drug Enforcement Administration (DEA) (no Flickr)
Federal Bureau of Intelligence (FBI) (Flickr)
Immigration and Customs Enforcement (ICE) (Instagram)
National Security Agency (NSA) (Flickr)
Secret Service (Flickr)
Supreme Court (Historical Images) NOTE: This photo collection is clearly marked as requiring permission prior to use in, well, pretty much anything. You could probably squeak by giving it to your kid for a school report, but seriously – find another source or ASK and wait for permission. (It is include for those authors who do, in fact, have a need such that they are willing to ask and wait for permission.)
US Marshals Service (Flickr) NOTE: Copyright information is not clearly stated. Some digging will be required to determine, or contact them directly to request permission.