I think it would be cool if there were "adventure games" that were based around time, ie. the player has various stated or unstated goals, and depending on what he does in his environment different things happen at the end of the interval. But then the next interval starts and the changes are incorporated in the game. Simplest example: You have one day to save the world. If not it explodes. But things can be more complex and more real. Imagine something like a dating game / The Sims game Your girlfriend-to-be is coming round but your house is a mess. Maybe the first time you can take her out for a meal, but eventually she will come round anyway. So the player has a certain amount of game time to sort out the house as best possible. What does the player prioritise? If he tidies the living room, but leaves the bathroom messy she may walk out in total disgust at his animal like standards. The player can be given a "in-game" week to meet some goals etc. Depending on if they have the story goes one way if not it goes another.

Sim City had things like this. You could de scenarios where you're the mayor of Chicago during the fire, or you have the rebuild Hiroshima after the Nuclear Strike. You get something like two years to have a functioning, profitable city, and you have to amass a certain amount of money during that time. I think. It's been a while.

Also see The Legend of Zelda: Majora's Mask. It was based on a three-day period, at the end of which the moon crashes into the city and everything is destroyed. You learn a magic song that lets you turn back time, so you can live those three days over and over again. Items you get, you can keep, and some other events are permanent, but the clock is always ticking (except in dungeons), and there's only so much you can do at a time. Neat game.