AssaultCube is a popular cross-platform first-person shooter with pretty low hardware requirements, with a fast gameplay and many modes – including the classic CTF, TDM, FFA, or the popular TOSOK (Team One Shot One Kill), LSS (Last Swiss Standing), or HTF (Hold the Flag).
World of Padman (or WoP for short) features a cartoon-style approach, with maps, characters, weapons and sounds all based upon the Padman animation series.
Eschalon is a turn-based RPG (role-playing game), which tries to reproduce the feeling of classic RPG games. It's closed-source, available for Linux, Mac OS X and Windows, and it comes with a demo too. The full version is available as a download for $19.95.
Wolfenstein: Enemy Territory
A true classic and one of the most played online first-person shooter games, Wolfenstein: ET was supposed to be released as a new mod for Return to Castle Wolfenstein, but the single-player part of the game was abandoned and it was released at no cost, as a standalone multiplayer game.