Minecraft is a fun arcade game where you explore lost worlds, kill monsters and uncover secrets. Download here for Windows, Mac and Linux. This is the The Bountiful Update.
Minetest is an infinite-world block sandbox game and a game engine, inspired by InfiniMiner, Minecraft and the like. It has been in development and use since October 2010.
Battlefield meets Minecraft. FPS shooter with online multiplayer action in a sandbox world.
Software that can be used as an alternative to Infiniminer: