God I love Minecraft. It probably was the first gaming experience that really sucked my time away. I spent days in that blocky world.
Minecraft was always a social game. Even if I was playing a game on my own it was in a social context, where I'd talk about what I'd done the next day at school, or learn how to do something else from someone talking about their exploits. The game, because so little "lore" of any kind existed within it, had this oral tradition around it, that made just talking about it addictive. It made us all story tellers.
Of course there was the more explicitly social aspects as well where you would get into a world together with friends and do whatever the hell you wanted. There are to this day so many different ways to play the game.
You could get pretty much anyone to play and have a good time in the game. The learning curve was fantastic. The basic knowledge you need to play the game, the controls and ideas, could all be picked up in a matter of minutes, but there was still the extensive discoverable knowledge, like crafting recipes, or the ways the world was generated and the landscapes it contained. Even after you had explored all of that there was still the whole world of building knowledge, using all the things you knew how to craft. There's the architectural approach, the engineering problems, and even the computational with redstone and the like.