1. Tremulous
Tremulous is a free, open source game that blends a team based FPS with elements of an RTS. Players can choose from 2 unique races, aliens and humans. Players on both teams are able to build working structures in-game like an RTS. These structures provide many functions, the most important being spawning. The designated builders must ensure there are spawn structures or other players will not be able to rejoin the game after death. Other structures provide automated base defense (to some degree), healing functions and much more...
2. Nexuiz
Nexuiz is a free first-person shooter video game developed and published by Alientrap Software. It is free and open-source software. Nexuiz uses the id Tech 3 Quake engine and is heavily inspired by Quake.
3. Warsow
Set in a futuristic cartoon-like world where rocketlauncher-wielding pigs and lasergun-carrying cyberpunks roam the streets, Warsow is a completely free fast-paced first-person shooter (FPS) for Windows, Linux and Mac OS X.
Speed and movement, that’s what Warsow is all about. Like a true cyberathlete you jump, dash, dodge and walljump your way through the game. Grab those power-ups before your enemy does, plant the bomb before anyone sees you, and steal the enemy’s flag before anyone knows what’s going on!
4. Assault Cube
AssaultCube is a FREE multiplayer first-person shooter game, based on the CUBE engine by the team at Rabid Viper Productions. Taking place in realistic environments, with fast, arcade gameplay, it's addictive and fun!
With efficient bandwidth usage, it's low-latency and can even run over a 56Kbps connection. It's tiny too, weighing in at a lightweight 40 MB package available for Windows, Mac and Linux. On the correct settings, it can even run on old hardware (Pentium III and above).
5. Wolfenstein: Enemy Territory
Wolfenstein: Enemy Territory is a free and open source multiplayer first-person shooter video game set during World War II. Enemy Territory uses the id Tech 3 engine. The game has two teams (Allies and Axis) and your requirement is to defend or destroy mission objectives.