The common understanding is that humans are attracted to primal instinct of power and domination, and firing a bazooka missile into someone's chest is a great way to fulfill that urge. Naturally, we become used to that urge and desensitized by it, causing children to look at violence less critically than they should be. I see one big flaw in this argument. How often do you see a kid punching someone in the face because he had a primal urge to dominate somebody? I would say very rarely. How often do you see someone throw a punch because they feel threatened? All the time.
The urge to dominate is not nearly as strong the "fight or flight" instinct. When we feel threatened, humans do one of two things. We fight, or we run. You don't stand there doing nothing. This is accompanied by an adrenaline rush that piques the senses and fires up the mind. Violence in video games (for the most part) is tapping into fight or flight instead of pure power and domination.
In the typical First-person shooter setup (and FPS is where almost all the controversy begins), it is you vs. an overwhelming number of enemies. Your job is to take care of the situation. Now, the first response to aggression is not "haha, yes, more people to kill and dominate," You may think it is. That's a trick your mind plays on you. In reality, your first instinct is to survive. The true goal of an FPS is not to kill everything. It's to kill everything, and survive. It's not just "kill". It's "kill, or be killed". The adrenaline rush of fight or flight is what gives tension to the gunplay. If you couldn't die in an FPS, the fun would diminish rapidly. The aggression that we hear about all the time is the fight side of fight or flight. It's your mind giving you the confidence you need to fight your way to survival.
There's a good reason why the survival horror genre is producing great games these in these past few years. The violence and blood and gore only adds to sense of doom and impending death that drives the player to keep playing. It also adds the flight aspect of the instinct as a crucial aspect of the game. Now, flight may be the only way out of a situation. In that case, running away from violence becomes as fun and suspense-filled as the violence itself.
I think that there are very few people who would judge a game's quality by how much violence is involved. It's the impetus to the violence that gives a game it's shine. Sometimes that's plot, sometimes it's simple survival, and sometimes it's just to rack up points. But it's almost never for the sake of violence itself. There are very few games that tell you to go kill everything because it's fun. There's almost always a compelling reason (that has nothing to do with reality) to engage int battle.
Granted, the Grand Theft Auto series changed all that. For the first time, a game rewarded the player for senseless acts of violence. You got money for every pedestrian you ran over, and you can mug people for spare change. There are consequences for committing these crimes, but they are easily disregarded. The controversy behind those games won't go away so easily. But the vast majority of games aren't like that.
When you look at violence in games through the lens of survival instead of the lens of domination, the effects of the violence also change. instead of being senseless, the violence is put into a context of survival. The outcome won't be kids shooting up stores for fun and profit, but kids who will start to fight when faced with flight. Assuming that connection can even be made (it can't, really, but I'm not out to debunk that here and now), the consequences are far less dangerous. There's a whole lot more to talk about when it comes to violence in games, but I think it helps to put things in a different perspective.