GEMpire is a simple turn based multiplayer strategy game, written in java, designed to be played over the internet in client-server fashion. It is a generalization of the commercial game Empire Deluxe for the PC. It consists mainly of a server, a client, a map editor, and a random map generator.
TuxKart is a 3D GoKart racing game with several famous OpenSource mascots participating. The game uses PLIB and OpenGL, and is portable to a wide range of OS's. There are several racecourses provided, with full information on how to add your own. Except for a few minor details, this game is essentially complete, and very playable.
Ren'ai/Dating Simulation Engine is derived from a type of computer game from Japan. The player controls a point of view (POV) game character, who interacts with other game characters in the hopes of winning the love of one of them. So far all of these games are closed source, and none have been translated into English. The Ren'ai includes a cross platform, internationalized game engine, on which dating sim type games can be played, plus an English based game to play on that engine.
omega is a complex rogue-style game of dungeon exploration. Unlike other such games, there are a number of ways to "win", depending on various actions taken during play. The ways you can get your name on the hiscore board include becoming the highest ranked head of a guild, sect, college, etc., as well as gaining the most points figured from possessions and experience. The game (via the oracle) may impose some structure on your exploration, but you need not follow all of the oracle's advice. There *is* a "total winner" status, by the way.