There hasn't been any conclusive evidence that violent video games cause violent behavior in the long-term. Quite the opposite, in fact. Violent Crime Rates have been on a general decrease since the 1990's. Since games can offer an outlet, people would rather go on a killing spree in GTA than they would in real life, because you don't have consequences in a video game.
The media too frequently makes the mistake of "correlation = causation" when it comes to video games and violent crimes. Just because a mass-murderer played Call of Duty, that does not mean Call of Duty was a factor in becoming a mass-murderer. By that logic, we should ban Water, since 100% of people who commit crimes also drink water.
"Never argue with stupid people. They will drag you down to their level and then beat you with experience."
-Samuel Clemens
