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 states 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.)
Note: The Smithsonian Institute, including the National Zoo, often has more restrictions than other government agencies, so please be sure to check the usage / rights page before using any Smithsonian images for commercial purpose. Book covers count as commercial purposes, but non-sponsored blog posts are generally allowed.
Nature, Parks, and Animals
Encyclopedia of Life Images (Smithsonian Institute is a participating organization) (Flickr)
National Arboretum (no Flickr, rarely updated)
Science, Environment, and Health
Food and Drug Administration (FDA) (Flickr)
Mine Safety and Health Administration (Flickr) – Historical Images
Smithsonian Institute (Flickr)
African American History and Culture (Instagram) (Note: As of fall 2015, it is still under construction.)
Anacostia Community Museum (no Flickr) (Note: Anacostia is a predominately black community in Washington, D.C.)
American Indian (no Flickr)