Anything you do has an influence on you, and how you think. Playing video games has an influence on you, yes. Playing violent video games will desensitize you to the violence you see. What may have shocked, scared, or made you gape at the beginning of the game now just makes you grin, or elects no emotion at all. So, in that regard, yes, video games affect people. But unless you're extremely weak minded, playing video games isn't going to turn you into a psychopath… and there's a reason for the ratings on games these days. Wolfenstein, Max Payne, Solder of Fortune, or any of their sequels, are not created for young children to play.
In order for you to go out, grab a gun, and blow people away, something else needs to be wrong. Playing a game isn't going to cause such an action, but it can most certainly be part of the cause. It can be one of the straws upon a person's back. What you do, what you see, what you read, what you listen too; it all effects how you think. Pile many factors together, and you get a changed mind.
Video games are simply the whipping boy for the modern parent, who quite frankly, is passing the buck. It's the parent's responsibility to raise a child correctly, to see that they have a firm moral and spiritual background. What we see are parents blaming the most convenient thing around, the video game. They're ignoring their own incompetence, and blaming a form of entertainment for their downfalls.