Before download or use, check for any copyright or usage restrictions. Most images are provided with the intent of limited educational and scholarly use, but that does not mean they can be reproduced for widespread use or in products intended for sale.
If you are using the image for a class activity or assignment, consult the Visual Resources Association's Statement on the Fair Use of Images for Teaching, Research and Study to see what kinds of uses are advisable. See especially Principle #4.
Resources for reading and links to previous conferences on copyright are available from the University of Oregon at Christine L. Sundt's Copyright & Art Issues.
Check the website of the museum or gallery that owns the work you wish to research. Basic information about the work, the artist, and possibly its provenance will be available through the owning institution, with more in-depth research and documentation available in their research collections (if they have any).
Some Selected Collections:
National Gallery of Art
Located in Washington, DC, this is the art gallery for the nation, but collects much more than US artists. Works are available to view and in many cases have a bibliography link to find more information.
Smithsonian Image Gallery
Over 138,000 images digitized from photographs, slides, paintings and much more. Searchable by using the AMP catalog (includes documents and other materials as well as images) or browse the groupings by type of original media, Smithsonian collection group, or most popular use.
Metropolitian Museum of Art
AKA "The Met", offering searches by object, date/era, artist, culture and much more.
Getty Art Collection
One of the premier art collections on the West Coast.
University of California San Diego Slide Collection
The images are NOT online, but if you need to know what they have before going to visit the collection, this is the search tool for you. Many of the items are held in the Arts & Architecture Library.
Walters Art Museum
Not only images, but background information about the work including conservation and exhibit history.
Victoria and Albert Museum: Access to Images
A massive, searchable collection of images from the collections of the V&A Museum in London.
LUCI--Materials held in the University of California system by seven participating campuses. Materials range from ancient Greek and Roman classics to California and public art. Be sure to read the page on 'How to Use LUCI" to understand the collection and get the best results.
Mother of All Art: Image Collections and Online Art--from University of Michigan offers links by geographic and genre headings.
New York Public Library Digital Gallery
A wide-ranging collection of images (photographs, prints, and more) from the massive collections held by NYPL. Sorted into subject-related collections or fully searchable from the home screen, these range in date, subject, media and purpose.
Visual Collections-- A collection of over 30 online collections assembled by David Rumsey and Cartography Associates. Most collections are freely available, but may require a one-time software download available from the site. Collections include cartography, fine arts, architecture, photography and other.
World Images
A collection being assembled by the CSU with over 65,000 images has a broader range of content, including political and cultural history. Tutorials are provided for maximizing your use of this collection. This is a growing project with subject-specific image collections planned.
WikiMedia Commons--An image and media collection assembled in the wiki format. Searchable by subject, type and collection. Verify usage permissions before download.
More links to collections, artists, and museums are discussed in David Mattison's article "Looking for Good Art: Web Resources and Image Databases, Part 1".