Video games help brain development, games like Minecraft and other games have been known to be educational, but other games that aren't designed to be educational can improve on basic skills and increase knowledge without them even realising it. Call Of Duty Black Ops may have violence and guns, but it also improves reaction times and increases strategised thinking. Other arguments say games are unhealthy because they can cause addictions and stuff. But in all honesty that's simply the parent's duty to take care of their kid and make sure they aren't on video games all day, of course, you can't just let your child spend all day on the computer. While it does provide benefits you still need to be active.
I guess it could help children learn things in a simulator sense. For example, last year, a kid learned how to drive a car to safety after playing Mario Kart on Wii. The kid showed that video games can be educational in a simulator sense because the controls on a simulator are realistic.
Because a game like minecraft will teach them teamwork because on servers kids have learned to work with each other to survive, Survival because they have to have food so they learn to hunt and they have to kill their foe to survive and tactics because they learn what each enemy does and the best way to deal with them and games like Portal/Portal 2 teach them to figure out puzzles with increasing difficulty that alone should be good enough a reason to tell your kids to play it.
I don't mean to be biased, but as a 14 year old myself I believe it depends. Like others have said, games like Black Ops don't but games such as Minecraft do. In fact, Minecraft is in ciriculums for over 600 schools worldwide and counting! Tell all your kids to play Minecraft!
Some scientists asks a couple of adults to play super mario for 30 minutes for the next month. When they checked their brain again, their problem-solving part of their brains grew. Adults are just like kids, they both have brains. And if kids' brains are developing, would it make sense not for kids to play?
All this does is puts kids in a trance and keeps them from being healthy. Kids need to be outdoors getting vitamin D and making there bones good and strong. When kids are on video games it makes them fat and they have a better chance of having a heart attack
Playing video games can help kids to develop their thinking, improve their problem-solving skill and build a lot of other pros but kids are not smart enough to handle an organized schedule to not let them play games too frequent which may subconsciously apply a video games addiction to the kids. In addition, playing video games is not one of the importances to undergo a normal and healthy life as a kid. What I am trying to say is that playing video games may make them have smarter brains but they still do not have to feel the need to say, "Mom, I'm going to play video games today and you can't argue anything about it because I am trying to develop my mind!".