As much as I love to compare Minecraft to Dwarf Fortress and have it be smacked down every time, I think it's kind of pushing it to start doing that every time the two are even partially mentioned together.
On topic(kinda): Minecraft almost certainly got its attention from being sold as opposed to being free. That is most definitely a huge factor in the attention it's been garnering.
Also, I think, it is popular because it feels like a fringe, unique game to the mainstream people. Like a scale.
Mainstream Niche
<-----------------------|----------------------->
^ ^
Minecraft Dwarfort
Most of the people who play Minecraft are more mainstream gamers. Minecraft is the perfect balance of an obscure feel, like the players feel like they're part of a niche and accessibility, so they don't get confused. They are completely unaware that they haven't even crossed the border into obscure and niche games. They feel like it's unique because the majority of them are only aware of Call of Duty 12 and such, when there are far more interesting and unique games farther to the right of the scale.
It's accessible enough to be played by mainstream people, and unique and niche enough for people to be like, "Wow! This is so unique!". It doesn't help their sense of entitlement though, but that's another story entirely...
This making any sense to people?
EDIT: cleaned up the scale