One of my all-time favorite computer games (though that is not saying much since I've only played like 3 or 4 computer games in my life) is Sim City. I've had Sim City 4 for a long while, but just this week started playing it (I had some free time these past couple of days). I love building cities from scratch, especially the transit system. The only other computer game I've spent significant time playing is The Sims, but even then I don't actually play the game... I just like building the houses.
Katie introduced me to Spider Solitaire, which I find somewhat annoying. I generally don't like playing games on the computer, but I do give my full endorsement to the Sim franchise.