I used to annoy my little sister by reading up on simple games with mathematically perfect strategies, then beating her every single time. Now she refuses to play with me. (E.g. Nim, and variations thereof. If you don't know how to play Nim, it's actually a pretty good example for this thread. The perfect strategy requires a certain amount of mental arithmetic and is non-obvious, so if you don't know it the game is pretty playable.)

Edit: In retrospect, I'm a jerk.