Frets on Fire is an open source clone of the ever-popular PlayStation 2 music/rhythm game Guitar Hero. It’s a free download and is available for Windows, Linux and the Mac, though the Mac version is experimental.
Hedgewars is multiplatform, a free turn-based blast-em-up in the vein of Worms. It features a wide range of weapons, multiple maps, and excellent graphics and audio. Offers single player, multiplayer, and (in theory) multiplayer over the internet modes.
The Battle for Wesnoth is a game that every strategy fan should play at least once. Though it is turn based, its heavy emphasis on combat keeps the game moving and avoids the boring lulls that other turn-based games are susceptible to. It also boasts a unique set of mechanics that allow for a much broader range of conflicts, far beyond the typical “kill everyone” or “survive for X minutes”– objectives that are common to most strategy games.