When we started our lab in 2007, we expected that in a few years massive sets of images of artworks (and other areas of visual culture) will start become available from major cultural institutions. So we focused on developing methods and techniques for their analysis (what we call cultural analytics), while waiting for these collections to become available. The wait is almost over - these collections are here. (Unfortunately right now museum interfaces often tell web visitors how many "objects" they have in their database, but not how images, so some of the numbers below are approximate.)
Examples:
MoMA - currently 33593 images online
www.moma.org/explore/collection/
Brooklyn Museum - probably 97,000 images online (their interface says that they have that many records but does not explain how many images they have)
http://www.brooklynmuseum.org/opencollection/collections/
SFMOMA - all 6,038 works in the collection are online:
http://www.sfmoma.org/projects/artscope
BBC Your Painting - currently already 110,000 images online from UK national collections, with the aim to reach 200,000
http://www.bbc.co.uk/arts/yourpaintings/
Cleveland Museum of Art -
currently 65,000 images online.
Whitney Museum, NYC:
not clear how many images are online but looks like a lot
Powerhouse Museum, Sydney - somewhere between 98,000 and 170,000 images online (their interface does not explain how many images they have)
http://www.powerhousemuseum.com/collection/database/
More and more museums offer their data via APIs:
List of museums offering API
The first museum API was developed some time ago by Powerhouse Museum - currently it offers access to 90,000 thumbnails:
http://www.powerhousemuseum.com/collection/database/download.php