If I really had to pick one (and I do!), I would have to pick the Pythagorean theorem. I have a few reasons - including memories of friends giving hour-long proofs of this theorem, memories of high school math, memories of a seven-page paper on Pytagoreas, etc., etc. I guess the main reason is that (besides right triangles being the sexiest triangles, and thereby making all right-triangle theorems the sexiest theorems) it's one of the more commonly used theorems, and it comes in handy a lot in geometry - which is where I think I'll end up teaching first.
Pythagorean Theorem: $ a^2 + b^2 = c^2 $
- For some reason, I had a little bit of trouble with getting this to work, so I hope everything went through all right.
