Why FOSS games?
Minetest is the first game on our list. Minetest is perhaps the most complete alternative to Minecraft, which is considered a "near-infinite-world block sandbox game and a game engine." Multiplayer games and subgames are supported, and there are a range of terrain generators and various default biomes available. For making mods in Lua, it also has a really user-friendly API.
Minetest is open source under the LGPL, and is written primarily in C++ so it's fairly fast compared to some others written in scripting languages. Minetest runs on Windows, OS X, Linux, Android, FreeBSD, and possibly other operating systems as well. Check out the source code on GitHub.
OpenTTD is an open source copy of Transport Tycoon Deluxe, a business simulation game where you manage a transport company in pursuit of maximum profits. In addition to the original game, OpenTTD provides several new features and improvements.
RollerCoaster Tycoon 2, the 2002 simulation game that allows you to develop and run amusement parks and, more importantly, design and build roller coasters, is an open source revamp of OpenRCT2.
The Dark Mod
The Dark Mod is a first-person stealth game that's reminiscent of the cult classic Thief. Set in a dark fantasy world, you play a thief who must steal goods---among other acts of thievery---while evading capture by guards. It offers heart-pounding fun with lots of replayability.
Alien Arena, formerly CodeRED: Alien Arena, is a fast-paced multiplayer first-person shooter in the vein of Quake and Unreal Tournament. While there are objective-based game modes, fragging is primarily about (killing your opponents). And if you're competitive, you'll love the global stats leaderboard.
If you are into open source software, you can also read