My kids have been playing it for years. I think DS was 3 and DD was 4. They are now 7 and 8. I would tell people "hey my kids really love Minecraft, yours would probably like it too" and I got blank stares. Now everyone is obsessed with it.
I sometimes wonder if Minecraft is the reason their WISC PR scores are both so high...maybe it does actually raise visual spatial ability and they've both certainly spent enough time on it.

The reason I don't object too much is because it does seem to involve a lot of creativity and problem solving, unlike other games like Super Mario Bros. It also makes a good bribe. DS gladly does things he normally wouldn't want to do in order to get "mods" as a reward or "screen time." Today he was enthusiastically talking about how he's going to clean his room so that he can get the "galactic craft mod" whatever that is.

They play it on the PC and often Skype with cousins or friends to play together.

They play on Dh's server in their own worlds so no one tears anything down unless they invite their friends/cousins in and things get out of hand.