I'm not going to sugar-coat this. In my opinion, illegalizing violence in video games would be no less than ridiculous.
For one thing, I'll reinforce cheating-is-good's point. There have been times in my past when I was picked on and bullied, and I was terribly depressed because of it. Now, without an outlet of healthy relief, I would have either gone on a rampage and killed my bullies or simply held it in and became self-destructive. Instead, I got on Grand Theft Auto and went on a killing spree in an environment where it didn't matter, just to relieve some stress. Killing in an environment that is virtual and has no consequence versus actually causing harm to fellow human beings... I'd say the video game offered a healthy outlet, wouldn't you?
For another point, I'd simply ask what illegalizing it would accomplish. I admit, there are some people who murder or act violently because they saw it on a video game. The number of people who do this is outstandingly insignificant when compared to the total numbers of copies sold of the game in question, but the occasional murders can be blamed on violence in gaming. Now, we illegalize these video games. ... Does anyone really think that would stop people from playing them? These kids that thought it was okay to go out and kill people because they saw it on a game... you think they are going to be careful to enough to avoid something just because it is illegal? Illegalizing the games would not prevent psychopaths from getting their hands on them, it would just prevent sane people from using games as an outlet, which is totally counterproductive and would probably lead to even more violence in the real world. Basically, if illegalizing violence itself didn't help, what makes anyone think illegalizing potential causes of it would do any better?
Plus, as Shadow_Lord has correctly pointed out, mentally stable human beings do not try to reenact what they saw on their gaming consoles. Mentally stable people realize that it is just a gaming console. Mentally unstable people may misunderstand that.
Let's look at less violent video games. Off the top of my head, I'll just go with any Superman video game. Mentally stable people will realize that it is just a fictional game. Mentally unstable people might kill themselves by thinking they can jump off a building and fly. Therefore, Superman encourages suicide. Does that mean it should be illegalized? No, of course not, that would be absurd. So would illegalizing violent games.
Finally, I would argue that illegalizing violence in video games would actually provide another excuse for lazy parenting. The parents could simply tell their kids to follow the law, not actually having to worry about whether their kids understand why it is a law in the first place. Think about it. The kid isn't going to learn that violence is wrong, he's going to learn that video games are wrong. That doesn't improve his well being in any way. Why do it?