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Sauerbraten (a.k.a. Cube 2) is a free multiplayer/singleplayer first person shooter, built as a major redesign of the Cube FPS. Much like the original Cube, the aim of this game is not necessarily to produce the most features & eyecandy possible, but rather to allow map/geometry editing to be done dynamically in-game, to create fun gameplay and an elegant engine. The engine supporting the game is entirely original in code & design, and its code is Open Source (ZLIB license, read the docs for more on how you can use the engine).
AssaultCube is a FREE multiplayer first-person shooter game, based on the CUBE engine. 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).
Paintball 2 is a fast-paced virtual paintball game based on the Quake2 engine, with capture the flag, elimination, siege, and deathmatch (free-for-all) styles of gameplay. Players are split into two teams, armed with paintball guns, and head out to capture the other team's flag. One shot knocks a player out, and players must wait 60 seconds to respawn. To win a round, you must knock out the entire enemy team.