The 2D solar system simulator is kind of neat, I remember doing that too.

The reason that I lean towards some sort of math problem or physical simulation is that when I was in high school I was always wondering "Where's the application of this? How good do I have to be before I can do anything with direct application?" in my programming classes. With something like a 2D solar system simulator you can say "Hey, I built something that charts the courses of the planets based only on the laws of physics and my programming skills, how neat is that?"