This is by far one of my favorite games to date. it might not be exactly up to par with the latest in graphics, but in my opinion it surpasses most current gen games in terms of creativity.
The game offers a classic mode, in which you can build things with different types of materials online with other people, and a survival mode, in which you.. well.. survive.
the original game was minecraft classic (although it was then called minecraft) and it is a very simple game. You start in a sort of cube, with limits on how high/low you can go and how far in each direction you can go.
In survival mode, however, there are no limits in the directions you go. The terrain generates itself when you move in a certain direction. (The high/low limits still exist, though) you start off with nothing, and build your way to success. You craft your own weapons, tools, even buildings. But watch out, because at night monsters come out and attack you (hence the name "survival mode")
heres a video of a castle a friend of mine and I have built recently;
Theres a wide variety of different materials you can use. You can even have a bed! crafting items is a big part of the game, and the minecraft wiki site has a lot of useful information incase you ever need to find something out about the game.
The game is by far one of my favorites and definetly a recommendation from me. It currently sells for $15, but when the full game releases it will be $20 (it's in beta at the moment)