Personally, when I play a game I'm not basing my enjoyment on whether or not it's violent, or how violent it is.
Games, in general, are based on competition. In video games that competition plays itself out in the form of triumphing over the enemy, overcoming impossible odds, gettin' the girl, saving the day, etc. And these themes are rooted in childhood.
As boys, we men would play cops and robbers, cowboys and indians, and "war". It's in our genetic makeup and mental wiring. It's just how God made us. And that has carried over into the video game realm where our fantastical adventures can be brought to life in an astoundingly visual and audible way.
Boys dream of being the hero in a big war, the star quarterback in the Super Bowl, the Top Secret undercover super-sleuth agent that's got all the neat gadgets, cool cars, big guns, and winning personality. And in that we are drawn to games like Medal of Honor, Madden, Unreal, Final Fantasy, and Morrowind.
And because of our insane imaginations, we dream up things like the Borg :robot: and MechWarriors, giving over to games such as Deus Ex and...well, MechWarrior.
And then of course there's the thrill of being able to do something that in real life we would never dare due to either moral, societal, or physical constraints. Enter in Thief, Hitman, and Max Payne.
With that said, I do have my own boundaries which I will not cross. Two examples are The Getaway and Grand Theft Auto (any of 'em, pick one, but especially the most recent versions). In these two games all moral inhibitions and convictions must be thrown aside to participate in the degrading debauchery that is the game itself. From the 'F' word to pickin' up hookers to regain health then killing them to get your money back...it's simply disgusting stupidity run amok. Sure, you can throw an "M" rating on it, but the question is why make that crap in the first place?
Many games made today are not for kids. But that doesn't mean that they're to be regarded as Anti-Christical and blasphemous, leading to school shootings and mental instability.
Violence is not why we love these games so much. It's being able to live out those boyhood fantasies that, before today's technology, were simply...in our heads. Let me tell ya, there's not a lot much cooler than being able to take down the Nazi regime in Medal of Honor without ever breakin' a sweat ;).