Can I levitate an object without using an electromagnet?

The references in other answers to the Wikipedia pages about Earnshaw's theorem and Magnetic levitation are right on; you absolutely cannot have stable, static magnetic levitation using only ferromagnets. However, at the time of my posting, both other answers contain misinformation.

Kakemonsteret's answer is incorrect*, because Earnshaw's theorem is not the end of the story. If you violate the assumptions of Earnshaw's theorem, its conclusions are no longer valid. There is a special kind of magnet Earnshaw's theorem didn't consider, which you can use for stable, static magnetic levitation: a diamagnet.

Superconductors are strongly diamagnetic, but I suspect using a superconductor is an unsatisfactory solution, unless you have liquid nitrogen on tap. Weaker room-temperature diamagnets like bismuth and pyrolytic carbon don't support much weight, but they will levitate forever and don't require cooling, electricity, or attention.

user879's answer links to the excellent Wikipedia page on magnetic levitation. I'd like to emphasize that this page explicitly discusses diamagnetic levitation, which I think is the closest answer to the spirit of your question: a special type of magnet that makes an object levitate without using an electromagnet. However, the answer goes on to state that a bowl of [ferro]magnets would also work. This is false.

I spent a full summer in high school trying to float a tennis ball covered in fridge magnets above a bowl lined with fridge magnets. I failed; I wasn't violating any of Earnshaw's assumptions. Years later when I finally learned Earnshaw's theorem, I was relieved to realize my failure was predictable, since my goal was provably impossible.

So, buy some strong ferromagnets, buy some strong, light diamagnets, scale down your design's ambitions to something very light, and start building your decorative item.

Don't put your credit cards or your hard drives near it.

*EDIT: This answer has been updated, and now mentions diamagnets.

EDIT: I can't believe I forgot to mention my favorite aspect of Earnshaw's theorem: it proves there's no such thing as solid objects! This is the single most obvious everyday evidence for quantum mechanics. If you see an apparently static, stable object that isn't held together by gravity, then it can't be modeled as a collection of point charges interacting through Newton's laws and Maxwell's equations.

Earnshaw's theorem proves that using only static ferromagnetism (like refridgerator magnets, which have a very slowly changing magnetic field) it is impossible to stably levitate against gravity.

http://en.wikipedia.org/wiki/Earnshaw%27s_theorem.

Diamagnetic materials might be used to levitate objects.