I was watching Cindy play some Civilization 3 last night before falling asleep (I'm tired all the time), and I went to lay down for a few minutes to think about a gaming concept that I had that's more in line with evolution. Civ and its brethren are closer to what I imagine than anything else, so let's start with that.
Diverging, let's talk about a game like Guitar Hero. Super fun, but completely static. There is constant input that you get better at handling (can't really call it "responding to" after you have the note chart memorized). Anyhow, that's the thing. It's fixed input that you get better at.
I'd like there to be a game that is more like "evolution." That you have to adapt to your environment, but you have to also try to stay as adaptable as possible. For instance, fish do well, and humans do well, but if either air or water were to disappear, we'd both be out of luck. I know that we each need both to some degree, but I think you understand what I mean.
So, what do I want? Random worlds, and no fixed anything in there. I don't want the Koreans to be good at Science and whatever else (as in Civ 3), I want everything to completely depend on the environment. Human ingenuity is a powerful thing, and I'd like to see more of it.
If something as "fixed" as Guitar Hero can get people to innovate their own tapping methods, I'd like to see what people come up with in a more open ended game - a completely open ended one.