Spore

Even though Spore has been out for a while, I still feel like it's worth talking about. For those of you unfamiliar with Spore, it's a "god-game" where you play as evolution. You start out with a microscopic organism that you can customize and as you progress, your creature gets more options for customization. Eventually, your creature will sprout legs and swim to land. Then you can further evolve your creature to have more parts and customization options. You progress to be able to have more creatures in a pack and eventually, a tribe, and then a civilization.
The game is constantly changing and everything is procedurally generated so the animations and music are generated by the computer rather than created by designers. The thing I love most about Spore is the Creature Creator. You can design the ugliest, most impractical creatures that would never survive in the real world or build the most powerful intimidating killing machine you can imagine. Really the whole game comes down to whatever the player can imagine and that is really cool.