There are different kinds of violence, too. I mean, you take a Battlefield, Call of Duty, or Left 4 Dead type game and violence is kind of the point. But a game like L.A. Noire, contains violence as an option, but isn't the point of the game. You're mostly interviewing people and searching for clues, and in most cases, violence is one of several options. Then there are your open-world games such as Fallout 3 or New Vegas that fall somewhere in between?sure, you're going to run into violence, but you can get through large portions of the game without having to kill anyone. I'm not a big fan of the first type I listed (especially since they usually feel more like "shooting gallery" games than anything else), but I love the other games I listed. I guess I'm just a fan of simulated worlds wherein you have some sense of agency beyond deciding which target to shoot next.
Games like Baldur's Gate that use the old top-down party-control type systems are frequently violent, as well, but the violence is less visceral, as you're generally looking at things from a distance. Same with most strategy wargames. Then there are games like the Civilization series, where I've played through many sessions without any violence at all.
And finally, you have your city-building/Sim-type games where there's rarely any violence.
And this comes down to what I love about gaming in general: there's something for just about everybody, if one knows where to look.