If I made a game...

Ok, the truth is, I don't have time to build a game. But that doesn't mean I can't think about it. I'm going to work through some of the game ideas I have here.

What kind of game would it be?

Story
I like games with stories. I have no problem with Tetris or Lumines or Sokoban or whatever puzzle-game-of-the-month is out there, but for me, a game is not interesting unless it has a story. This can either be a simple scripted story (as is the case in most adventure titles, for example) or an emergent story that arises from my actions while playing. In either case, however, I need to feel like I am participating in some form of narrative arc.
Consistent World
Essentially, I play games for the same reason I read science fiction and fantasy books: I'm looking for an escape from my current reality. I want the game to take place in a relatively rich, self-consistent world. It needs to be "rich" in that must have rules that are complex enough that I can't guess them easily. It needs to be "self-consistent" in that the rules should make sense when I do understand them, and should be applied equally to all entities in the game.
AI
I mean this in the sense that is meant by the game development community rather than the computer science community. In other words, the game entities that I can interact with must at least potentially behave in a way that I could attribute human (or the equivalent) motives to. They should have as wide as possible a range of ways to interact with the world (ideally the same set that I have in game) and should use these in ways that I would in the same situations.