I loved playing Spore, where you basically play through the evolution - you can create your own ufo-like creature and then you will have colonies, tribes, cities, then you go out into space. My favourite stage was the tribe stage - every time I succeeded at chasing the enemy away, I made them dance around the fire. No matter which creature did that, it was funny.

My other favourite is Sims. I started with Sims 2, and now it's Sim 3. I've always liked these kinds of games where you can create something (or someone) on your own.