In Europe you can secure a copyright on a photograph of a work in the public domain (e.g. a Rembrandt). Provided that you've kept the source away from cameras, you can enforce your copyright on the grounds that any instance of "your" image were either copied illegally, or created illegally.
The same does not hold true in the US, thanks to Bridgman Art Library vs. Corel
"Bridgeman Art Library v. Corel Corp., 36 F. Supp. 2d 191 (S.D.N.Y. 1999), was a decision by the United States District Court for the Southern District of New York, which ruled that exact photographic copies of public domain images could not be protected by copyright in the United States because the copies lack originality. Even if accurate reproductions require a great deal of skill, experience and effort, the key element for copyrightability under U.S. law is that copyrighted material must show sufficient originality."
http://en.wikipedia.org/wiki/Bridgeman_Art_Library_v._Corel_....
Of course, this is one ruling by one court. It could be challenged. In the meantime, it looks like the SCOTUS has taken the view that copies can be yours, even if the original isn't.
The practical difference is that the originals are in the genetic makeup of billions and circulating freely, whereas notable paintings tend to be unique and tightly controlled.