There have been a number of attempts to redesign and copy Minecraft outside of Mojang. Some have been con artists. Some have been mod developers who wanted more. However there have also been those who have been inspired by Minecraft and have designed completely new games as a result, e.g. Terraria.
A new game is Patterns by Linden Lab, the developers of Second Life. Patterns works in terms of triangles, not cubes. Players can find resources and use them to built constructions. It has stronger physics than Minecraft. Therefore, gravity sucks and constructions will collapse if they are not appropriately supported. The first release is soon and reviewers suggest that they will follow the "Minecraft Model" in terms of payment (ie. cheap for alpha version, more expensive for the finished game).
A review - Patterns Could Be the Next Minecraft - IGN
The official Patterns page - http://lindenlab.com/products/patterns