Wow. It's amazing to me that the first two noders here have seized upon the theorem as a theorem. For me the most interesting thing about Fermat's last theorem has always been the story that goes with it.
Fermat asserted it was correct, and that he had proved it, but he never bothered to write out his proof. He wrote a note in the margin of a book saying, Demonstrationem mirabilem hanc marginis exigiutas non caperet, "I have a miraculous proof which this margin is too small to contain". He never bothered to write the proof down. And so for 350 years people have been trying to prove something that was, to him, too obvious to bother with.
Sorry for the lack of gratuitous links.
February 27, 2001
gratuitous links update
I just made some updates to this writeup, such as adding the actual text of Fermat's marginal note (in Latin). I have decided to respect the mood I was apparently in back then, and left all non-gratuitous links out. This is not my policy, as you can easily see at my other writeups (if only I had linked that, you'd be there now!)
In the meantime, I am leaving gratuitous links out of this writeup as my interpretive dance statement on nomespace pollution.