Can I take a photo of a copyrighted painting?

...yes. Well, kinda.

I'm not a lawyer so bear with me.

If it's for your own private collection, it should fall under fair use. Fair use can also cover you if you want to critique or comment on the work. If you wanted to sell the photo or even publically display it, you would need permission from the copyright holder. Some works of art will fall under public domain, especially those old enough that the original artist has been dead for a long time.

It also depends how much of the work you photograph. If you are standing far enough back that the work is not by itself, or is even simply in the background, you are okay.

It is tricky when you're taking a photo of a painting, sculpture, or a product. It comes down to whether the photo is a derivative work. If too much of the original work is copied, the original copyright holder can sue the creator of the derivative.

This article seems to summarize that yes, a photograph will be a derivative of a work, even if you are creating a 2-D photography from a 3-D sculpture. (You couldn't go the other way, either, say, making a 3-D sculpture from a copyrighted photograph). This means whoever made the copyrighted thing that was photographed will retain the rights.

Newspapers usually will have fair use -- if it's "news" you will have leeway to report on copyrighted material (If Jay Leno does a monologue about Des Moines, the Register could reprint part of it even though Leno's monologue is copyrighted). So, fair use will also depend on the amount of the original work used. Again, comment and criticism will give you some leeway, too. As long as you don't use too much of the original. And make sure to credit the creator.

More helpful info here.

So, to sum up, shoot away when it comes to copyrighted material, but if you're going to reproduce or publically display it, be careful who owns the copyright of that sculpture.