When it comes to really old art, it will be out of copyright itself, as it predates all relevant laws. However, the photographer may have rights to the photograph. In general, if it is a straight ahead shot that merely reproduces the painting and adds no artistic or journalistic aspect of its own (and contains no persons etc) then it also would not have a copyright.
The relevant laws are a bit convoluted, and have evolved a great deal over time. So hard and fast blanket statements are hard to make. Short of consulting a copyright lawyer (that's in all of our budgets, right?), you need to familiarize yourself with the law. To that end, on the left hand side of the screen and down a ways, you will see a section titled Resources. Copyright Info is the very first link. You probably want to look at the Trademark link as well.