My favorite theorem is the Pythagorean Theorem. It is much better than EVAN'S FAVORITE THEOREM_MA375Fall2008walther.
(No seriously, I chose it before looking at his page) --
It's one of those theorems that is surprising at first. When I saw the proof of it I was pretty amazed. See image here.
If I couldn't choose that one, I would probably choose the four color theorem, because I think it's kind of interesting since it's something people can relate to, and it's an interesting graph theory problem.
.svg){kind=link}