There isn't enough evidence linking video games and violence to even start that discussion, particularly when films and images of far more graphic violence are readily accessible. The answer to the problem seems to be the same as the answer to concerns about TV rotting your kid's brain in the 1960s: personal responsibility. If you're a parent, pay attention to the ratings, research the content of games online before you buy them, and above all, know your child's sensitivities and limitations. If you're in doubt about the effect of a game or other piece of media, say no.
Saying that video games cause behavior problems means that "kids who play violent video games HAVE behavior problems". So, no. Some kids have behavior problems. These kids with behavior problems may also play video games. Kids have had behavior problems way before video games were around. Should you blame comic books, tv programs, music, or even classic violent literature? Nope. A rational person (i.e. a person without behavior problems) of any age is perfectly capable of understanding that video games have no consequences and real violent behavior does.
They CAN cause them, but mostly don't. It's true, teenagers are impressionable. It's true, video games are really violent, but honestly, take a look at history. This facade of "peace" is neither usual nor lasting from an historical point of view. Several generations have had their young ones assaulted by, not war games, but REAL ACTUAL HONEST-TO-GOD war, and the human race is still here to prove they successfully grew old and multiplied.
As for the normal point of view, usually a teenager who is prone to delusions will be affected by violent games, and usually a teenager who is not, will not.
Being exposed to violence in video games will, long-term or short, cause children to adhere to violent behavior. It's like moving from Texas to New York. When you first move, you may have a Texas accent. After living there for long enough, you'll start to have a New York accent. People, human beings, adapt to their environment, their surroundings. Playing video games with violence will cause a child to reveal a violent nature. Some kids more than others. Those who are naturally aggressive are still going to show more of an aggressive behavior.
No, slow internet does. But in all honesty I don't think they are inherently bad for /teens/, as they should know by then what is socially acceptable. Children might be a totally different story. For the mass majority it is fine, but it really depends on the maturity and mental health of the teen in question, though I think the final decision should go to the parent on these matters.