I was discussing this topic with several other friends today: when it's your turn to watch the baby, what computer game do you play?
I have a night shift from 8 to about 12 to watch the baby and the best game I can play is Civilization IV. It's a little older now but it's still a good game and the turn-by-turn basis gives me a lot of time in case I need to stop and attend to him. Also Civ IV is can be played almost as well whether you have just a keyboard or just a mouse, which is an important factor when you have to do your turn one-handed (while bouncing on a big rubber ball holding the baby). Also, the game takes many hours to finish and that is just what I need.
My friend Eric is/was quite into World of Warcraft, but when the baby cries, he put his priest character into "follow" mode. Unfortunately, that doesn't always work so well, when the others need your help. E.g., they're off fighting a creature and you're just standing there while others are begging you to heal them. So, I won't mention what his character's name is...
Another friend plays a version of Half-Life--I think it's Team Fortress--where you can turn your character to Observor mode, thus essentially making your character invulnerable but ineffective in the game. Your teammates still probably won't appreciate you taking yourself out.
Anyway, I've played Civ IV to death and new I'm looking for another building/management strategy game. I hear good things about Caesar IV, so its next on my list.
Computer games for new fathers