Public domain means images no longer under copyright. That includes images from before 1923, images taken by agencies of the federal government, or images 
with open use licenses. Most images on the web are still copyrighted. For more information, see: Public Domain and Fair Use
Creative Commons licenses allow for various degrees of non-commercial sharing with attribution. Most Wikipedia images are either CC or Public domain.
Fair Use means that a copyrighted image might be used for non-profit educational or literary purposes (such as a parody) but this is an individual call, and can lead to copyright trouble. This video, for example, was taken off YouTube but allowed to be replaced there because it was an educational sound substitution project.
Copyrighted images are nearly everything that is not public domain. You should not use them without permission.
Wikimedia Commons — Most images are under the Creative Commons license; They can be used, with attribution, for educational and non-commercial purposes.
Library of Congress Division of prints and photographs — many but not all are copyright free; anything before 1923 is public domain, and of course anything by the government, including the FSA collection
British library — Millions of free images from the UK and Europe
Open Culture — Outstanding collection of free films, movies, audio files and open courses.
US Geological Survey — Scientific photos — geology but also plants and animals.
US Dept. of Agriculture — Agricultural Research Service photos
US Fish and Wildlife Service — Scientific photos of plants and animals.
US Government — general collection of photos
National Oceanographic and Atmospheric Administration — Scientific information
National Aeronautics and Space Agency —Scientific information
Centers for Disease Control — Scientific information
New York public library — archive of 180,000 photos