Minetest
Minetest was created by Perttu Ahola, aka. celeron55.
It's an open-source sandbox voxel building game (engine), very similar to Minecraft, except that it was written in C++ and doesn't require Java to work. The game is free and fully modable, players can download various mods from the official forum, or write their own with Lua.
Due to the fact that Minetest is an engine rather than a closed game, players can create their own customized Minetest game variations with their own mods and settings - aka. Subgames. The default (installed) Minetest game is a subgame too, also known as Minetest Game.
More information here: Subgames
Minetest can be played in singleplayer mode or on servers with other players, all available servers are listed by the game's client. The client also offers a posibility for players to host their own servers.
In-game cheats are supported too.
Download: minetest.net/downloads