No, violent video games should not be banned. I am a person who does not believe in censorship for the most part. When the label on a game says "Mature" or "18+", it means "for mature people" or "for people of age 18 and older."
Now, for some reason, parents in America are morons(as a whole, not every single parent), and allow their small, impressionable, sheltered children to rent these video games with the rating "M" on them, and then complain when they see people being blown to bits or chopped in half. That's just stupid.
If a label says a game is too mature for your child, then DON'T RENT IT. They have warnings there for a reason. But America just needs something to blame for the laziness of parents in this new generation, and they chose violent video games.