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Free Open Source Games

Flesh Snatcher
A first-person shooter game with a zombie theme, written in Java using the jMonkeyEngine.

The Battle for Wesnoth
Free, turn-based tactical strategy game with a high fantasy theme, featuring both single-player, and online/hotseat multiplayer combat. Source is available for Windows, Linux, MacOSX and there are older versions for other platforms. There is also a user made content editor (UMC IDE).

Red Eclipse
Multiplayer first-person shooter, available for Windows, GNU/Linux, BSD, and OSX.

FlightGear
An open-source flight simulator that supports a variety of popular platforms (Windows, Mac, Linux, etc.) and is in active development. Licensed under the GNU General Public License. Uses Open Scene Graph, Boost, and other C++ libraries.

Teeworlds
A free online multiplayer sidescroller game with a classic/retro look, includes a map editor. Versions available for Win, Mac, and Linux. Languages used appear to be primarily c/c++ and python.

Chaotic Rage
Written in C++ as a development of an older 2D game, now uses OpenGL. A third person zombie shooter game. Binaries are available for Windows.

GNU Chess
An older chess game written in C with a primitive visual interface, but supporting more advanced gui interfaces such as XBoard.

AstroMenace
A 3D scroll shooter game written in C/C++, available for for Windows, Mac OS X and Linux. Source appears to be licensed under versions of both GPL and Creative Commons.