You start in a massive, randomly generated world, and pretty much do whatever you want. The hook is that you can burrow into any surface, as well as build anything out of the materials you mine.
There are random mobs running around which drop unique items, a day night cycle, gardening, farming, livestock, crafting... and every week the guy is adding more.
Multiplayer is now in the game, in a rudimentary form. You can connect to a persistent server, mine resources, and build structures with other players. There are no mobs or persistent inventories as of yet, however. Notch said these will be added very soon.
If you played the previous free version, the new "alpha" build is much more structured, requiring you to gather resources and craft them into building blocks and various weapons/armor.
Some screens (EDIT: Replaced with some great stuff GAFFERs have found and made):
The website:
http://minecraft.net/
You can check out the free version there, but the 10 euro (about $12 US) Alpha (which is called "Survival") is what contains the real game... which includes all the stuff I mentioned above. There are PC, Mac, Linux and Browser-based builds.
IMPORTANT: The game is currently 10 euro(around 12-13 US $), but will go up to 25 euro in the near future (most likely when multiplayer is implemented). So grab it while you can while it's half price!
For GAF multiplayer servers, please refer to the OP in this post:
http://www.neogaf.com/forum/showthread.php?t=403071
It can be a bit confusing to figure out, so here are some starter guides:
http://www.minecraftforum.net/viewtopic.php?f=35&t=17013
http://www.minecraftforum.net/viewtopic.php?f=35&t=17021
And the crafting section of the Wiki (definitely needed, just keep this up in your browser as you play):
http://www.minecraftwiki.net/wiki/Crafting
EASY QUICKSTART GUIDE FOR NEW MINECRAFTERS BY ME
As soon as you start your world, find the nearest tree, stand next to it's wooden trunk, point at it, and hold down the left mouse button. You will punch the tree until it breaks, and a wood chunk will fly out that you collect by standing near it. Continue punching the tree until you've destroyed all the wood blocks and collected them all. Note that you can punch pretty far from where you're standing, so just keep looking up and punching.
Once you have all this wood, press "i" to bring up your inventory. Place the wood blocks from your quickbar into any of the crafting squares. To the right, you'll notice that planks will appear. Right click on these planks until you've converted all the wood into planks, then put them in your inventory.
Place 1 plank unit in each of the 4 crafting squares, and it will make a work bench. Put this workbench on one of your quickslots (the bottom-most row of slots).
Now, place 3 plank blocks on the upper left crafting square, and 3 plank blocks on the lower left crafting square. You will see a stick appear in the right most box. Right click this 3 times to create 12 sticks. Put these in your inventory.
Now, press the hotkey (1-9) where you placed your workbench. This will put it in your hand. Right click on the floor in front of you, and this will place the workbench.
Right click on the placed workbench. This is the main crafting device in the game. As you can see, there is now a 3x3 grid with which you can now craft in, allowing for more complex devices to be made.
Place 1 stick in the middle bottom square, 1 stick in the center square, and 1 plank in each of the top squares. This will create a wooden pick axe. Drag this into one of your quickslots.
Now you're ready to mine! Make a note of where you came into the world, as when you die you will return here and have to make your way back to wherever you came from. Now, wander around the world looking for coal. Coal looks like a regular gray stone block with black splotches on it. Once you find some of this, mine as much as you can by holding the left mouse button over the block with your wooden pickaxe equipped.
Once you gather a few coal, open your inventory and place a few sticks in the bottom left crafting box and some coal in the upper left crafting box. This will make 4 torches. Put these into your inventory.
This will get you set to build a house, which you will need built before nightfall. I tend to burrow into a mountain side, and make a small cave with which to hide out in. Consult the above crafting wiki on how to make a door, or you can just fill in the door with dirt/rocks at night to keep the baddies out.
For every brick you destroy, you gather whatever the brick was made out of in your inventory. Put these bricks on some hot keys, select them, and right-click to place them. This is how you build structures.
Now prepare for your life to be sucked away.
And, finally, the creator of one of the most important game created in the past five years, Notch:
Personally, I can't stop playing it.
