Origins
I started Minecraft after playing some Infiniminer with a couple of people from TigSource. I 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 I wanted to change and stuff I wanted to add.

I had recently quit my job as a game developer to be able to focus more on indie game dev during my free time, and I was looking for a new game to develop. I had a few ideas floating around, but most required really long development times.
These two factors led to Minecraft.

Development and philosophy
Waterfall is dead, long live agile!
I've got a few plans and visions, but my 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 I want to add but think I might forget.
I make sure to play the game a lot, and I've built my share of towers, and flooded my share of caves. If something ever doesn't feel fun, I'll remove it. I believe that I can combine enough fun, accessibility and building blocks for this game to be a huge melting pot of emergent gameplay.