It might seem that I'm a bit late to the party with this, but I can assure you that I bought Minecraft a few weeks ago and was happily digging and building until my computer stopped working*. The laptop I'm using at the moment is not capable of running Minecraft in a playable fashion, I'm missing it.
Thankfully Rock, Paper, Shotgun, and Penny Arcade have picked up the ball, and I can keep abreast of developments on Notch's own blog.
Minecraft is a Java based game that seems to defy any sort of pigeon-holing. Its played from a first person perspective but its not an FPS. You can construct any edifice you like but its not a city builder (a la Sim City). There's crafting, but its not an MMO, there are dungeons but its not an RPG. Minecraft is a strange beast and has more in common with Dwarf Fortress than any other game, instead of being in control of a settlement of dwarves though you are an individual. It is a sandbox in the truest sense of the word, and it may very well be the first true sandbox in existence.
You start with nothing, literally. Absolutely nothing. From these meager beginnings you have the means to get everything else. If you want wood, go and hit a tree. With this wood you can craft planks, from planks you can craft a crafting table which opens up more crafting options to you with its larger crafting grid. You can now make sticks, essential in the construction of tools which allow you to harvest other materials such as stone, coal, iron and eventually diamonds.
The freedom of movement is unparalleled as well. Once you have a spade (wooden ones don't last long, stone lasts longer, iron longer still and diamond the longest of all) you can dig down, or horizontally in any direction. The practically infinite world (surface area of approximately eight whole Earths) is explorable in every direction. With enough stone you can build a tower to the top of the sky. With enough patience you can dig down to the bottom layer of adminium (beyond which lies the void). Or you can wander the surface and take in the amazing scenery.
You can also choose to do this in peace without the nightly invasion of zombies and skeletons, or allow such incursions to curtail your nighttime activities through the use of 4 different difficulty settings (peaceful, easy, normal, or hard), or you can join one of the many servers which are springing up all over. These multiplayer servers are places where players can work together to create truly monumental constructions or greif each other into oblivion. A Minecraft sport has already been developed called Spleef, which involves players attempting to drop each other into either water or lave by removing the blocks beneath their feet in a specially constructed arena. For a better idea of what is achievable in multiplayer Minecraft its a good idea to watch the various videos on the homepage (and click a few random ones too, I discovered some gems because my 4 year old has the attention span of well, a four year old).
The really amazing thing about Mincraft though is not the sheer freedom available to you, or the endearingly simple graphical style, its the fact that it is not finished yet! Indeed it is still in alpha. Updates (until recently, see below) have been pretty much weekly, with new features and crafting recipes being added continually. Last weeks addition brought us a craftable compass so we could explore freely without getting lost. Only Notch himself knows where the game is going to end up in its finished state, but he is at least willing to be guided by the growing community with regards to features and additions to the game. Personally I'd like to see a kind of meta-game developed for Minecraft which allows for trade and the transfer of character's inventories between the participating servers but that's just me others have much more in depth ideas and they're worth having a look at on the official Minecraft Forums.
Notch, the one man show who started programming Minecraft as a hobby about 18 months ago, made it a full time career about 9 months ago, and is now hiring staff and starting up a game development company (lots of meetings hence less development time) with the proceeds of what started out as a hobby. As a lifelong gamer who has perpetually aspired to do something just as creative and profitable as this, my hat is well and truly off to him.
Minecraft can be acquired for 10 euros and this gives you access to all the future updates for free and unlimited downloads and installations. Lets support Notch as he grows this game into something truly original and groundbreaking (pun intended) which we haven't seen since Love.
*It might be my PSU which is a simple fix, or it could be my MoBo, which isn't. and would basically mean a new computer (apart from monitors thankfully, as I have those) hence the inclusion of a button on the right there through which donations may be made. (alternatively you can click some of the google ads if you don't want to donate directly).