In general, yes, images are protected by copyright law. American copyright law protects any original work that is fixed in a tangible medium of expression, which includes photographs, drawings, paintings, and other types of artwork. 

Copyright protections last for a fixed term, so all images eventually enter the public domain and become freely available for anyone's use. Creators also sometimes license their work under Creative Commons licenses, which allow anyone to use the work in question, so long as they comply with the terms of the CC license.