I have 4 step daughters, one of them is heavily into video games, fighting games mostly, like Tekken and Mortal Kombat types. If it were my choice she wouldn't get to play them so much. Unfortunately it's her mother's call, and being a democrat she doesn't monitor the games very well.
Personally I think it is better to expose a child to violence in movies and games so that they are better prepared for coping with it when it happens in real life. At some point they are going to be watching these movies and games anyway, so why not when they are younger?