I played Unreal Tournament and Rune with my dad when I was like, eight. All the time. He took me to see war movies when I was in elementary school as well, and seriously, I didn't become violence-obsessed or anything like that. It all depends on how you treat the game, I guess. And, of course, you would know your kids best, etc.
Now that I'm thinking about it, being a girl might've made a difference. Girls (in my experience) didn't talk about flak cannons or rocket launchers, or how you could beat someone to death with their arm/leg in Rune, so I didn't. Games were things I talked about with my family pretty exclusively. I definitely do not remember being like some of these manicky kids I hear on xbox live.