OpenArena is a community-produced deathmatch FPS based on GPL idTech3 technology. There are many game types supported including Free For All, Capture The Flag, Domination, Overload, Harvester, and more. There are 17 unique player models to choose from and 12 weapons.
Though other FLOSS FPS like Xonotic seem more polished and complete, this game is really fun.
Furthermore it is possible to run a vast of Q3A-Mods, which in my opinion makes OpenArena one of the best games to start with, if you are looking for a free arena shooter.