I'm sure you've heard it before: a violent video game caused some previously doe-eyed child to grow up to be a horribly violent, sadistic psychopath. Well, if video games generally considered to be violent can affect people's behaviour, why not ordinary video games, too?
Need For Speed - involves driving in illegal street races and trying to escape pursuits with the cops. Needless to say, I can't drive.
Yu-Gi-Oh! Nightmare Troubadour - involves saving the world by playing children's card games. Except I don't even own any yu-gi-oh cards in real life, let alone use them to save the world or anything heroic like that.
Final Fantasy Tactics - In this game, you move characters around a board and perform actions such as attack, magic, etc with them. Clearly a bad influence.
Guitar Hero series - Devil's music. Enough said.
And anyway, how broadly are we to define "violent video game"? Many video games are "violent" in the sense that they involve killing people, even if they're not gory. Eg:
Age of Empires - a historical game where you can be different civilisations who pillage other civilisations. Oh, wait, usually people who are againt violent video games want to drag us back through history and think imperialism is good. My bad.
In my view, even if there is a correlation between violent video games and violence, it's like saying there's a correlation between who plays FIFA and football fans. Well, you're less likely to want to play FIFA if you're a non-football fan!