My cousin had one that used to smoke, but he trained it out of that and got it doing exercise instead. Brilliant.
I never got hooked on The Sims in the same way, something to do with being a decade older possibly, but probably because I use my computer for loads of things now and not just games -- if it just sat in a window and talked to me occasionally I'm sure I'd still have it running.
Actually, there's an idea. How about a little person that lives in your filesystem? You could make files that he could eat to train him to hang around in the same kind of places, teach him to write you documents and leave them on the desktop, and clean up after himself. It'd be an application that ran at human speed, not just as fast as possible.
Wouldn't it be weird to navigate into a little used folder and find him there with another little computer person from a friend's machine who'd emailed herself over, and they were making even littler computer people together? [This post exists because the title of Dan Hon's The Sims post is Little Computer People. It reminded me.]