Of about 150 entries at the first seven day first person shooter development jam (7DFPS), so far I could identify two prototypes that have clear open source licensing in their code and run.
Note that this contest did not require sources to be released, only 19 entries had theirs released at time of writing.
Video: 7DFPS Cannonball Z Gameplay
Cannonball Z is a game where you shoot zombies with cannonballs. It features randomly generated maps.The source code is in the .zip file. The engine uses a BSD license. My code is GPL and my assets are CC BY-SA.
Video: 7DFPS: OxyFPS
OxyFPS is a simple first person shooter with the restriction of being in an oxygen-lacking environment.You are on an airless planet with only a suit, a crossbow and a tank of air.Your objective is to survive as long as you can while the corporate goons that caused this terraforming catastrophe hunt you down.
Then there's also Jedi-Academy--Renaissance, which I haven't been able to compile yet and Zombies in the Dark, which is only indirectly GPL-ed by being hosted on Google Code.
By the way: I participated in a project with my beginner Blender abilities but only the art assets are freely licensed.