Using the loose definition of a "video game", but I've been obsessed with "Words with Friends" (link is to iTunes) for the past week. Basically, it's Scrabble, played at your own pace with friends (or strangers) over the internet. You play a word, an dit notifies your opponent, and then at their leisure they play a word, and then you're notified. Simple. It's a game that was just made for that type of "play for 3 minutes whenever you get a chance" type of gameplay.
If any other iPhone owners out there want to play, my username is TheBobmanNH