Minecraft uses a massive 3D map, 128 segments high and god only knows the width and depth - it actually generates the terrain as you explore, so it might be more like a limit with the amount of data your PC can manage.
Anyway, if you wanted to make a limited size world of cubes, I would start by making a big array, say 128 high by 1024 wide and 1024 deep. Then I would make spheres inside that data, using a 3D distance check - so a bit like having the whole world filled with different sized balls. You could set the balls to different materials, like iron ore, small balls of diamond etc. Then I would have all the map data shift down, so the bottom is completely solid and varying in height, like a terrain should be. If you imagine these balls are made of Minecraft sand, they would all fall down and generate a landscape.
Then once you have a basic, solid terrain, cut spheres out, have the spheres move around while cutting to create tunnels.
With that you might end up with a decent Minecraft style world - not as complex as the real method, but it might be enough to get started with.
Health, Ammo, and bacon and eggs!
