It's not correct to attribute the voxel game genre to Minecraft. It's just the first game of the genre to reach a considerable level of success.
Minecraft is just one of many games that were directly inspired by the underground hit Infiniminer.
Minecraft is just one of many games that were directly inspired by the underground hit Infiniminer.
http://en.wikipedia.org/wiki/Comanche_series
Also interesting (historically) is 'Rescue on Fractalus'. Not just for its cheesy name, but also due to its reliance on fractals to draw 3D mountain sceneries:
http://en.wikipedia.org/wiki/Rescue_on_Fractalus!
Edit: videos of both games:
http://www.youtube.com/watch?v=M8opv5u9nf0
First time (as a kid) was shocking...
(To add to the confusion, this particular game, Ace of Spades, actually is voxel-rendered.)
It is however thought that John Carmack's next engine after the Rage engine may include honest-to-goodness voxel rendering: http://en.wikipedia.org/wiki/Id_Tech_6
Historically, Carmack has had quite a lot of influence on both the hardware and API vendors, so it will be interesting to see if he can spearhead more mainstream movement towards sparse voxel octree rendering: http://youtu.be/THaam5mwIR8
The iPhone wasn't the first smart-phone, it wasn't even the first touch-screen smart phone, but most people (correctly) give it credit for popularizing the style, and creating a new "genre" for smartphones.
Edit: Well, ok, I don't want to put it in such absolute terms. But I do think that Minecraft deserves quite a large chunk of attribution for the genre.
Minecraft is also not a voxel renderer. Voxel renderers typically work by casting rays against the grid. Minecraft draws the blocks with rasterized triangles, using a hardware-accelerated 3D API (LWJGL), just like almost every other 3D game.
In other words, there is practically no interesting overlap between what NovaLogic was doing, and what Minecraft does.