This game is amazing!!! I play it myself, and unfortunately agree that it is addicting. The game is almost 100% manageable for any age kid at any age, but at younger ages in strict moderation because I have a sibling that will not get off it (9 yrs old)! For little kids put it on peaceful (for Survival mode) because the monsters can scare the life out of almost anyone, which is why I'd suggest you only let them play Creative mode at that age. Survival should start at about 7 yrs.
By the time that they are 10 is about the time you should let them start to play on public multiplayer servers, just make sure that they have decent moderators and don't prompt them to buy things.
By the time they're getting through the first year of middle school (7th grade) you should loosen up on watching every single thing they do on minecraft (for protective moms- all of you others probably did that was probable ages ago!) You probably shouldn't let your kids on the hunger games servers until you've let them see the movie or read the books. The thing with public servers is that they could see anything if it doesn't have a proper moderating system.
When learning the controls, it can be very frustrating trying to figure it out for the first time, and until you're in the habit of laying your left hand on the keyboard in the WASD position :). I had to go on the wiki and figure out the basic controls.
For small children, (5-7 yrs.)this can instigate some agitation trying to figure out the controls, but can help develop their creative and basic critical thinking skills. You can expose your kids to this under the proper modifications. (Peaceful survival or creative)
For the 2nd biggest minecraft crowd (8-14 yrs.) this can also instigate amazing creative thinking, and for educators can create excellent teamwork if you create a private server for your students. Moderate exposure.
For 15+ it can still instigate creative thinking, but if you give them too much exposure they will either sit glued to the computer screen all day, or come up with a good plenty of ways to outsmart your original plans for their minecraft-ing, ranging from going on forbidden servers, to creating things that you didn't intend for them to even think about in the first place. This can become slightly dangerous, but they need to learn. These kinds of things can vary between boys and girls.
Speaking of YouTube, this can be a two faced nightmare. There are some players that will make tutorials and not use inappropriate language (Ethoslab is one, he is an amazing minecrafter), but there are a good plenty that will curse out the wazoo (wazoo is a funny word- BACK TO THE POINT.) like Skydoesminecraft and ASFJerome. Bashur is a questionable one, he can give some good laughs but he will curse jokingly when he pretends to play another character, like his "talking dog" Pooface, who will say what he wants to say when he wants to say it.
Now let's talk mobs. There are friendly mobs; Villagers, Cows, Pigs, Chickens, Ocelots, Bats, Iron Golems (when you don't attack their villagers) and Snow Golems. and Horses. There are also evil mobs; Zombies, spiders, cave spiders, skeletons, wither skeletons, slimes, endermen, lava cubes, wither and Ender Dragon, the two latter being by choice. Then wolves, which can be tames into domestic dogs, will try to kill you if you smack them before they're tame. All of these can be killed with anything you're holding in the game, depending on what and with how many hits. The evil mobs will be turned off with Peaceful mode on.
Alright, I feel like I've covered most of the bases. Hope this helps!