The New York Sun has a piece today on "how the proliferation of digital cameras is changing the museum experience for visitors and the institutions themselves." Some New York museums, including the Jewish Museum and the Whitney, don't allow any photography. Others, including MoMA, the Met, and the Brooklyn Museum, do allow photography, with restrictions (e.g., no flash).
The article does a pretty good job summarizing the relevant law:
"Generally, works of art that were created before 1923 ... are not subject to copyright law. For newer works that are covered, there is a distinction between owning a work of art — the physical piece itself — and owning the right to copy it, which is usually held by the artist or his estate. MoMA and the Met do not hold the copyrights to newer works in their permanent collections. Allowing public photography of this work is generally justified as fair use, depending on several factors, including the quality of the image and whether it is for private use."
One quibble: it's not whether a work was created before 1923 that matters; it's whether it was published, which often turns out not to be an easy thing to determine.