http://www.utsystem.edu/ogc/intellectualproperty/copypol2.htm#test
This is a nice summary of the "4 factor" fair use test.
Here's my interpretation of how we would argue for fair use in the case of a photograph of a still-copyrighted artwork, like a painting or sculpture in a museum.
1. What is the character of the use?
Our use is nonprofit and educational. Because the photo of the artwork would naturally be accompanied by an article about the artwork, our use is criticism and commentary. Notice that even commercial use can be o.k., if the use is generally educational, commentary, criticism.
2. What is the nature of the work to be used?
In general, this factor will not help us. The nature of the work is 'imaginative'. I'm not sure if a work of art in a museum is considered 'published' from this perspective or not.
3. How much of the work will you use?
Here we are in very good shape. A small web image of a statue or a painting is a relatively small use. A recent U.S. Appeals court decision (Arriba) said that search engines can use thumbnails of web photos that are copyrighted, for example, in Google's image search.
This is similar. A small web image is not a full and complete reproduction of the work.
4. If this kind of use were widespread, what effect would it have on the market for the original or for permissions?
This seems to lean heavily in our favor. It seems unlikely that our use would detract from the market for the original or for permission for real reproductions (posters and the like), so long as our images are kept small. If we offered massive and extremely accurate digital files which would permit the end user to print a nice poster, this would weigh against us.
But a small web image is not going to damage the market for posters.
--Jimbo