What's the goal of Minecraft and what can users achieve in this world?

The thing about Minecraft is, unlike most games you set your own goals. Here's a list of common (and uncommon!) things people have done with Minecraft:

• Building a massive structure
• Recreating real-world objects
• Survival (Deleting map upon dying)
• Making amusing videos
• Creating an adventure map for others to play
• Getting all the achievements
• Proposing to your girlfriend
• Achieving difficult things in the game through ingenuity
• Computation
• Blowing stuff up!

The mechanism that keeps the game going is your own desire to complete the goals you've set yourself, and pure, red-hot addiction.

Edit

Some additional stuff people have done:

• Walking and walking and walking (thanks SevenSidedDie)
• Build an epic railway
• Make music
• Find the Far Lands

Minecraft 1.9+

In Minecraft 1.9 and beyond, there are villages, strongholds, abandoned mineshafts and nether ruins to explore. In particular, strongholds will contain portals to The End, in which players can fight The Ender Dragon, a 'boss fights'. The second 'boss fight' has also been added, The Wither. This makes exploration a key part of the game, as well as combat. 'Hardcore Mode' (world deletion upon death) is also an option if you're after a challenge.

A creative mode has also been added that allows players complete freedom in constructing large structures, compartmentalizing that aspect of gameplay.

It's a sandbox - there is no strict goal other than to play around and survive. You can even keep dying all the time if you like, you always respawn, you just lose what you were carrying, so even that is optional!

It just provides a set of gameplay mechanics (mining and crafting, not surprisingly) that let you muck about, build stuff, discover things, defend yourself, etc.

I thought it sounded pointless until I bought it because I was bored and was surprised to find that it's worryingly addictive ;)

At the moment (with beta 1.5) there is no goal beyond surviving, earning a few achievements and what goals the user sets themselves.

These might be building a creeper proof house, finding all the gold on the map, exploring the entire world etc.

What keeps the game going? Whether the user has met their self imposed goals or not.

I have heard that there is meant to be a goal built into the game, but I haven't got a link to it at hand. From my point of view I'm quite happy with the goallessness of the game.