I run a family/friends server and all 4 of my kids play, and my wife, and my brother as well as a couple friends. My youngest is 4 and he just plays single player on peaceful cause mobs are a bit much for him. Man, some of the things he comes up with and build is pretty damn amazing (admittedly, I could be bias). He made a water slide down a hill with a boat and a bucket of oil. Science! My 6 year plays on our server when he can and is equally amazing. My wife gave Minecraft the stink eye for some time till I sat her done and said, Do me a favor, play for two hours and then go back to not liking it after you have tried it. Bout a week later she set up a server for everyone.
We also run a homeschooler server for the local area homeschool kids for kind of a safe haven, "social" interaction. Gives those kids a stable spot to play together as homeschool kids are generally scattered through the city and not easy for them to get together on the proverbial playground.
There are a number of studies out there about kids and video games. The shorthand punchline is children with unfettered access to video games actually are the opposite to the myth that it makes them violent or addicted. When they only have X amount of time to play, kids tend to obsess in between times. My daughter is a good example of this. She plays for a while, then wanders off to read a book or play outside. The gated effect has been nullified and she doesn't wander around waiting for that time she can play and freely walks away when asked cause she knows she will eventually come back to it when she feels like it (yanno, after chores and school. I'm not a totally cavalier parent). Studies also show how kids who play games, even violent video games, and generally more even keel and less quick to anger or violence. The thought goes that they deal with the highs and lows, the rewards and frusterations of gaming. Damn you, creepers! Because they have that outlet and deal with stresses in game, it makes them more able to handle stresses of life. Is that a blanket statement? Course not, everyone is different and there is always the exception. But did playing too much Minecraft or MW3 make them that way? Hardly. You can't point a finger to one thing and say, listening to AC/DC made him that way. You need to look at the entire enviroment for answers. Parents, school, relationships, the individual themselves, etc. And if listening to Metallica or playing 2 hours of MW3 turns them into a little monster, then really anything could have been the tigger, not evil sinful gaming.
Everything must be examined that lead to that. But I digress, uh, alot.
I like the notion of unschooling. Bascially, give the child the tools and let them forge their path, help them where they need it, and they will learn everything along that path. They will, if they have the resources, get from where they stand to where they want to be. If they love something, they will get from point A to point B and learn everything along that path more easily and without reservation to get to that point. My 6 year old wants to play Minecraft and build a house like daddy. Cool, here you go and here is the basics. Run, kid. Before you know it, he is making plans, drawing out pictures counting blocks, asking me how to spell things like blaze or engine or obsidian. Sounding out words, learning how to read unfamiliar words, grasping cause and effect, doing math to divide the number or add the amount, hand writing out his list of things he needs...etc. All in a creative eviroment. Now, put a kid in a class room and tell them to learn math, read, and spell words for a worksheet. Bored kids don't learn or learn reluctantly. The best teachers are the ones that make it interesting or fun, right? My kid has accidently learned so many things along the way and was eager to do so, to get from point A to point B.
I'll stop now. Babbling again.