Offline computer (or console) game that progress over time

I know its not a good example to give on a computer post but take as example animal crossing that is affected by hours and days.

My question is if there are any games (can be on computers or consoles I like em all) that give you the feel of being lively... a game that change with time?

Im open to suggestions

@atomolog: What you're looking for are games that storyline impacts on the enviroment, GW1 did that, GTA4 did that when the bad guys bunt down Romans' apartment.

Can't think of any more games.

the harvest moon games. they are farming simulators...and strangely addicting. its not real time like animal crossing but things change throughout the seasons in a year in the game. stardew valley on the PC is very similar (though im not sure it has the time element. it wouldnt make much sense if it didnt though.)