Quake (series)!

Xonotic is a free (GPL), fast-paced first-person shooter that works on Windows, OS X and Linux. The project is geared towards providing addictive arena shooter gameplay which is all spawned and driven by the community itself. Xonotic is a direct successor of Nexuiz with years of development between them, and it aims to become the best possible open-source FPS (first-person-shooter) of its kind.

OpenArena is a community-produced deathmatch FPS based on GPL idTech3 technology. There are many game types supported including Free For All, Capture The Flag, Domination, Overload, Harvester, and more. There are 17 unique player models to choose from and 12 weapons.

Warsow is a completely free fast-paced first-person shooter (FPS) for Windows, Linux and Mac OS X, set in a futuristic cartoonish world where rocketlauncher-wielding pigs and lasergun-carrying cyberpunks roam the streets.

Red Eclipse is a fun-filled new take on the first person arena shooter, built as a total conversion of Cube Engine 2, which lends itself toward a balanced gameplay, with a general theme of agility in a variety of environments.

Cube 2: Sauerbraten is a free multiplayer/singleplayer first person shooter, built as a major redesign of the Cube FPS.

Unvanquished is a free, open-source first-person shooter combining real-time strategy elements with a futuristic, sci-fi setting. It is available for Windows, Linux, and Mac OS X.

Overwatch is a team-based shooter where heroes do battle in a world of conflict.

Urban Terror started as a realism based "total conversion" mod for Quake III Arena. Nowadays, Urban Terror is played using the free, stand-alone, ioquake3 engine modified, which doesn't require Quake III Arena, in addition to being an add-on to id Software's Quake III Arena.

Zandronum is a multiplayer oriented port, based off Skulltag, for Doom and Doom II by id Software.

Nexuiz was originally developed by Lee Vermeulen and Forest ‘LordHavoc’ Hale, who started Alientrap in the summer of 2002. The goal of the project was to create a high quality first person shooter that could be played freely across all platforms in one package: PC, Mac, and Linux. The engine that powered Nexuiz was Forest Hale’s Darkplaces engine.