Another view on why you might want to let your kids play video games. (If they want to, of course. :)
Relationship building does happen, even when video game playing is happening. It's much deeper than the gaming. It's valuing the interests of another individual. And how important is that when it's your child's? In my book, that is the utmost of importance.
The following article is an amazingly insightful recount of a 17 year old's experience with video game playing. He's a great writer.