The Getty Center has thousands of images of artwork and other cultural objects.
Artstor is a database of images of art work, art objects, cultural objects and architecture contributed by museums, archives and libraries from all over the world.
Conduct a "Quick Search" for artist, subject or work of art.
Conduct an "Advanced Search" and limit to artistic genre, geographic location and even time period.
Acceptable use of images (Artstor policy on permitted and prohibited use)
See the Artstor guide for help using the database.
Many museums, such as the Art Institute of Chicago and MoMA, and other cultural institutions have digitized items from their collections for public display on the web. See this list to find a museum of interest.
Google Arts & Culture has images from museums and cultural institutions around the world, such as MoMA, The British Museum, National Museum-New Delhi, and many others. Use the menu on the left to explore by collections, themes, artists, mediums, art movements, and more. (See Google's Art Camera project to explore some images in detail!)
Below are some other sites to try.
Search over 18 million objects--images, videos, texts, etc.--in the Smithsonian Digital Collections.