A quick update to yesterday's post. I came across another real time online game, Human Age. In this one you try to keep a caveman alive and help him (or her) to evolve through various ages of history.
Somehow, cavemen have jobs and markets and money, but other than that it's an interesting enough game. Each age is supposedly different, so by the time you figure out prehistory and start to get bored with it, you'll be able to move onto the next age. Each age has certain requirements for moving on...for cavemen, one of the requirements is learning how to make fires.
It's real time in the sense that once every day you get some benefit from what you're doing, so you should expect to check back in daily to adjust what's happening with your caveman.