I notice with a quick search that Minetest has not seemed to have been mentioned in previous discussions. Minetest is like a very basic Minecraft that is more like a base to build upon with mods. The API for mods is built right in, basically just dumping them into a particular folder and then turning them on within the game. These mods use Lua.
Also, it is completely free and works on Windows, Mac, and Linux.
They don't really have much in the way of tutorials to get started modding, other than this, which isn't all that much: http://dev.minetest.net/Intro
I have found the included aspects of the game (basic things like wooden pickaxe, stone sword, etc.) set up in the same way the mods are (it's actually a mod that way, an included mod), which is in the installation directory's games/minetest_game/mods folder. These seem to be a good place to start with figuring out how to make your own, besides what the tutorial and the lua_api.txt: http://github.com/minetest/minetest/blob/master/doc/lua_api.txt
Similarly, people release their own "games" which is basically just a particular bunch of mods together that make for a particular playing environment and setup. As I've said, Minetest is really a sort of base to build upon with mods to be how you'd like.
It's only in the past day or two
that I've really taken a look at Minetest and started to tinker with it. I can't say I know too much about it, but I thought it was something worth sharing. With the lack of tutorials, it is something that will take some figuring out, but that can be done with a bit of time and effort by anyone interested.