Wii Fit Plus has a math-fact game where you have to bump things with your hips to add up numbers. You have to have Wii fit first and the balance board. There are many other very fun/funny games in the fit series.
Lego games are usually ok because instead of blood and guts the characters fly into pieces and come back pretty quick (although I can see how some folks would say that is in fact bad)
Lego Rock band could be good, no fighting, this is funner if they are familiar with the songs I think. (requires at least a microphone)
Cars has driving, two person competitions and no fighting. My ds9 still plays it from time to time with dd, but it is not his fave as it is for younger kids.
There are many downloadable games for around $5-$10 that are like the old fashioned arcade games. Also all the mario games seem to avoid out and out violence, but there are things that are indeed out to get you, so you have to gauge your own child's reaction to each. They might be able to sample play some of these at a store, and reviews online often include some screen shots of what action is involved.
My kids probably watch a bit too much tv and games, but seriously have too many other things going on to have it dominate. For our ds with some social issues, sometimes the games are a great way to get a kid over to play and then things segue into other games.
Best of luck whatever you decide.
One thing you might allow is sort of a binge when they first get it (shocking I know) they can get a lot of the anxiety over playing out of their system in 1 weekend and then limiting their time becomes less of a hassle.
