I don't know if I have a favorite theorem, but I've always liked this one by Gauss:
- $ \sum^n_{i=1} i = \frac{n(n+1)}{2} $
I like this theorem because it's simple and useful and I also like the story associated with it's origin. The story that I've heard is that, when Gauss was very young, one of his teachers would occupy his students by having them add up a list of n integers. Gauss was able to do this in a matter of seconds and when the teacher asked him how he was able to add them so quickly he explained this simple theorem. I have no idea whether this is true or not, but either way I think it's a cool story.
