The game for this weekend is called Open Arena which is a Open Source version of Quake III Arena released just a few weeks ago in a new version. The game does not try to rebuild every inch and corner of Quake III but is still a pretty solid remake of the original game with technical advancements such as higher texture resolution and polygons in the character models.
You can play single player against bots or multiplayer against human opponents. Various game modes such as Capture The Flag or Death Match can be selected. The game is fast, has some servers with good pings available and is in my opinion one of the better games that are available freely on the web.