I'm a gamer, who grew up on Wolfenstein, Quake, GTA 1 & 2, Doom etc, and I turned out to be a very non-violent person.
My son (8,) and his sister (5) mostly play games that don't involve realistic violence (Terraria, Minecraft, Worms, the Lego games, Skylanders etc.) But I also let them have run arounds on my Skyrim, Dragon Age, and Fallout games occasionally, and they will battle monsters, animals, and raiders on those.
We don't have COD (my husband and nephew disparage it as "swamped by 12 year olds,") but for games like Battlefront, Battlefield, etc, we'll let them have a supervised twenty minute play online without the headset.They're both happy and well-adjusted children with extremely sweet, compassionate natures.
Honestly, I think you should do whatever you think is best for your child, but from everything I've heard, COD is basically made for pubescent boys, haha.
And as for people worrying about video game violence and the effect it has on children... We're currently in the least violent point in the world's history. A family day out used to be a hanging, they burned witches, flogged people, hung drew and quartered criminals, raped women, and treated human lives like nothing of importance, and I'm pretty sure that wasn't cos they played COD, seeing as video games didn't exist.
Within the context of a good home life, and played in moderation video games are not a big deal.
Also a PP said that "Loads of kids smoke and have sex at fourteen.... mine aren't doing that either." upthread, and I just have to mention that my mum didn't think I was having sex at fourteen either 