Minecraft is a little indie balloon swelling with popularity and success, and it just burst. The main server buckled under the weight of purchases, updates, and user verifications, and Notch has suspended all of those functions to get the game working again. Which means he's made it free, for a while.
Until he fixes it, Minecraft is entirely free , letting you play multiplayer survival mode like all the cool kids. Once it gets fixed , it'll start checking to see if you've paid, just like before. By then, you'll want to buy it. You can download the game at the Minecraft site .
The system fell over when Notch updated the server client to fix furnaces and add "sneaking" - features which I've been too excited to even try yet. He's now using Amazon Cloud to distribute the updates, and is working to get a new server and have someone with big brainy-pants write super sleek modern codez. (Read: He's doing magic to fix it.)
Remember to refer to the wiki for help with the game.