EA has released the original Command & Conquer for free to celebrate the pioneering real-time strategy game's 12th anniversary. Images for both of the game discs (GDI and NOD) are provided; I don't know how difficult they'll be to install/extract under Linux yet though.

Great free FPS game. It has in game level editor. Single player and multiplayer game play is available. Nice action and graphics.

Regnum Online is a free fantasy massively multiplayer online role-playing game (MMORPG) game (although premium content is available for enhanced game play) which runs on both Windows and Linux and I must say it looks really good.

Scorched 3D is a modernization of the classic DOS game Scorched Earth. It's a simple turn-based artillery game and a real-time strategy game in which players can counter each other's weapons with creative accessories, shields, and tactics.

Freeciv is a turn-based strategy game, with some real-time elements, in which each player is the leader of a civilization, fighting to obtain the ultimate goals of a nation: The extinction of all other nations, being the first nation to plant a colony in another star system, or survival to the end of the game.

Alien Arena 2007 is a free/open-source first-person shooter game based on source code released by id Software. Started by COR Entertainment in 2004, the game combines a 1950s-era sci-fi atmosphere with gameplay similar to the Quake, Doom, and Unreal Tournament series. Alien Arena is primarily an online multiplayer action game, although single player campaigns are also available against bots.

Creep Smash is a multiplayer tower defense game written in Java. It was developed by ten computer science students within a collegiate software project of the University of Applied Science in Stuttgart. The project requirement was to plan, design and implement a Java-based multiplayer version of Tower defense within 2.5 months.

"The free software community makes games, too. Among the more well-known ones is the Battle for Wesnoth — a turn-based strategy game with a fantasy setting. It doesn’t have shiny 3D graphics or cut-scenes, but it is an interesting and original game and is fun to play. This game is often simply called 'Wesnoth', and the package name is 'wesnoth'..."

This game has become very popular. It is a first person shooter game with elements of real time strategy. Free to download and open source.