Intellectual property (patents, licenses, copyrights) is a pretty tough concept to get your mind around, but you are in luck. As it happens, before I was a full time artist, I used to negotiate licensing agreements. True story. And since I received two almost identical inquiries involving this very subject in the last few months, I figured it warranted its own post.
In both cases, the requests boiled down to this:
they wanted to commission a piece of art from me and then sell reproductions of the image (one on jewelry, one as prints).
My short answer was "no" to both because, whether or not they purchase a physical painting from me, the image still belongs to me. That's where the "intellectual" part of intellectual property comes in - the idea (and execution of that idea) is my property. Yep. No matter what they pay for the paintings themselves, such payment does not include the right to use the images.
Still a little confused? No problem.
Think of it this way: Let's say you go to Borders or your local book store (they still have those, right?) and you buy a copy of Harry Potter and The Deathly Hallows. You own that physical book, that thing with pages (the "tangible property") - you paid for it. You may put it on the shelf or dog-ear the corners, sell it in a garage sale or even, God forbid, burn it if you want to. However, you don't own the rights to the IDEAS contained therein. You may not make copies of the book and sell them. You may not make a movie of the book.... unless of course you have permission from Ms. Rowling (customarily in the form of a license agreement and huge-ass amounts of cash going from you to her).
Art works very much in the same way. Let's say you pay me for a custom painting of your cat. No matter how much I charge you for that painting - you are only paying for my time, supplies and creativity, not for the rights to use the image. So even if I charge you an exorbitant amount, you still may not make copies, prints, Christmas cards (not even for your own use) unless we have a written agreement where I specifically give you those rights (which would be under a License Agreement). Yeah, I know, even though it's YOUR cat. Even if I painted from a photo you took.
2011 ADDENDUM: The reverse/reciprocal is also true: I have the right to do whatever I want with the image. As the artist, I may create prints, cards or another painting OR I may license the rights to someone else to make items using the image: rubber stamps, posters, car wraps, whatever. The recipient of the original has no rights outside of the ownership of the tangible, physical property (painting) and may not dictate what the artist may or may not do with the image. Even if it's a painting of YOUR cat. Even if it was painted from your photo.
Another intellectual property tidbit: you need to enforce your intellectual property rights or you lose them. That's why the Disney Corporation protects Mickey so vehemently. It's also why I do not ever make exceptions - not even for friends. I mean, you all saw The Godfather, right? "It's not personal, Sonny. It's strictly business."
Anyway, I hope this helped to give you a very brief overview of intellectual property as it pertains to questions I get asked pretty often. If you have more questions, let me know!