No clear answer, but evidence does exist.
I'm certainly no expert on the impact of violent movies, music and video games on the propensity of a person to commit acts of violence. Like many folks, for years I scoffed at the idea that there was a cause and effect relationship between violent movies and violent acts. I still believe that there is no link between violent movies and violent acts except in rare occasions when a person is already prone to violence and the movies feed their fantasies. I base this on articles written by mental health professionals.
The link between violent movies and violence-prone people seems to be the desensitizing effect of the movies. I saw the Wild Bunch when it came out in 1969. I was 19 years old. It was the first movie to use blood-packs to simulate a bullet penetrating a body and it was dramatic! It was praised and demonized by the public, elected officials and many mental health professionals. At 19 I had been shooting for 15 years and hunting for 9 years. Nevertheless, I winced when I saw the blood splatter from someone's back when they were shot. Now, 46 years and thousands of violent movies later, I can eat dinner and drink tomato juice while watching the most violent and bloody of battle scenes. (I'm not talking about slasher movies that I detest. I'm talking about war movies, COP shows, etc.) Violent movies do desensitize all of us to violence, but only a few are prompted to commit violent acts. As gun owners, we know that a free society cannot enact laws based upon the lowest common denominator.
The impact of violent video games and "music" that glorifies violence is far less certain. There is some evidence that participating in violent video games tends to remove our built-in safety valves, our natural resistance to killing our fellow man. Lt. Col. Grossman's books and others delve into this a bit. Grossman discusses the historical reluctance of soldiers to actually fire their weapons at the enemy, even when their own lives hang in the balance. He also discusses how this has changed with changes in infantry training. The switch from bullseye targets to humanoid targets during training resulted in a significant reduction in the reluctance of American servicemen to engage the enemy during the Vietnam War. The percentage of men that would not fire, or that would fire over the enemy's head, was dramatically reduced. This percentage was reduced further during the Gulf Wars when infantry training included simulated firefight engagements -- video games.
Thus, we know that practicing for battle using what are essentially violent video games has an impact on the willingness of ordinary men and women to use deadly force against other humans. However, to relate this directly to violence in society is problematic. Soldiers are being trained to kill the enemy, most of whom are trying to kill them or their brothers-in-arms, not innocent people on the street, or family members. Again, I'm a lawyer playing amateur psychiatrist, but I believe that the age at which this "training for violence" begins, the amount of "training" one receives, the amount of parental oversight and involvement the child/person receives, and the natural propensity of the child/person to violence are all factors.
As already stated, we cannot make gun laws or censor free speech (music, games, movies) based upon the lowest common denominator. Living in a free society has a cost, but that cost can and must be lowered by responsible parents doing the job of being mom and dad. If you love your kids, you do everything you can to protect them, to make them happy, to encourage them and help them build self-esteem. If you love them a lot, then you have the courage and self-discipline to do the hard part too, not just the things that make them happy. We learn to be responsible adults through both smiles and tears. To paraphrase a popular adage about combat training, cry a little as a child, or wail a lot as an adult. This holds true for both the individual as well as society.