Apps with 'Games support modding out of the box' feature
Minetest is a near-infinite-world block sandbox game and a game engine, inspired by InfiniMiner, Minecraft, and the like.
Rhythm game for Windows, Mac, and Linux. It features 3D graphics, keyboard and dance pad support, and an editor for creating your own steps.
Duality is a modular 2D game engine / editor combo, written entirely in C# and built on top of an OpenGL backend.