Open Arena is a free open source content package made with ioquake3 - an engine based on ID's Quake III engine, that faithfully recreates the original's feel and gameplay and, as such, is a fast-paced twitch-based FPS.
Instead of simply being a clone though, Open Arena adds new content to the game, such as player models, original weapons, maps and game modes, as well as including maps ported or recreated from other games in the Quake series. The engine is a significant improvement over the original Quake III engine and features many small performance and graphics tweaks, the most obvious of which are probably the Bloom and Flare effects. It also includes a custom soundtrack, which, though nothing special, is more than satisfactory in setting the mood for mindless violence.
The game has a strong online following, and you can usually find quite a few servers with 10 or more players at any given time of day, or if you'd prefer a single-player experience, the game includes some well programmed bots which can be set to any of the 5 typical difficulty levels found in Quake III (though they are probably a bit tougher than their Quake III counterparts).
All in all, Open Arena succeeds in its goal of providing a high quality, totally free multiplayer shooter experience.