Most of them (six!) are total conversions.
Total conversions: Q3 Rally, Urban Terror, Bid for Power, Combat, True Combat, Navy SEALs: Covert Operations
Partial conversions extending the core gameplay: David Hunter and Excessive +
You can play these mods via retail ("play") or Steam ("play through Steam") if you have a Steam copy of Quake III Arena. Also note that Quake III Arena and consequently its mods are mostly multiplayer-oriented, so you'll probably have to grab your buddies to play these mods (as zero to few servers are up at the moment).
Got tired of standard CPMA/QuakeLive ? Excessive Plus is for you, the fastest, most explosive 3D Action/Shooter (FPS) active mod in the world. It works with Quake III, IoQuake3, OpenArena and Xreal. What's possible on Quake3 excessiveplus ? Shortly, you can do anything with excessiveplus ! So join it, and enjoy it ;] "E+ is modification where all weapons and movement, are super-powerful and in every way excessive."
Mods install to the main game directory. You can also set your own mod launch commands on Desura, a short User Launch Options tutorial is here.