Minecraft was created by Markus Persson, it's bee under development since
May 10, 2009. The coolest fact about it is that it has been the mostly searched keyword in Google for 2011.
Origins
He started Minecraft after playing some Infiniminer with a couple of people from TigSource. He realized that a game that simple yet that dynamic had a lot of potential to turn into a really great game, and kept coming up with things he wanted to change and stuff he wanted to add.
He had recently quit his job as a game developer to be able to focus more on indie game dev during his free time, and he was looking for a new game to develop. He had a few ideas floating around, but most required really long development times.
These are the two factors that led him to Minecraft:
Development and philosophy
Waterfall is dead, long live agile!
Of course, I don't know what the Waterfall thing means but it's something big in it.
He has got a few plans and visions, but his only true design decision is to keep it fun and accessible. There's no design doc, but there are two lists; one for bugs, and one for features he wants to add but think he thinks he might forget.
He made sure to play the game a lot, and he has built his share of towers, and flooded my share of caves. If something ever doesn't feel fun, he'll remove it. He believes that he can combine enough fun, accessibility and building blocks for this game to be a huge melting pot of emergent gameplay.

He strongly believes that all good stories have a conflict, and that all good games tell a good story regardless of if it's pre-written or emergent. Free building mode is fine and dandy, but for many people it will ultimately become boring once you've got it figured out. It's like playing a first person shooter in god mode, or giving yourself infinite funds in a strategy game.. a lack of challenge kills the fun.
For survival mode, he'd rather make the game too difficult than too easy. That also means he's going to have to include some way of winning the game (or some other climax) to prevent it becoming too exhausting.
But if it's no fun, he'll redesign.
The future

He's planning on developing Minecraft until it's a finished complete game, with a downloadable client (with fullscreen mode), custom key re mappings and possibly modding support.
For as long as people enjoy and purchase the game, he will develop extensions after the game is done.
Once sales start dying and a minimum time has passed, he will release the game source code as some kind of open source. He's not very happy with the draconian nature of (L)GPL, nor does he believe the other licenses have much merit other than to boost the egos of the original authors, so he might just possibly release it all as public domain.
Well that's what he says, but, as I know the game is priced for $26.99