As someone else mentioned, Return to Castle Wolfenstein: Enemy Territory was created by ID Software as an expansion but released for free. It uses the Quake 3 engine, and was made by the people who make Quake and DOOM.
You can also try America’s Army. It wasn’t my style, but it might be yours. Slow Paced FPS.
To the guy that said Battlefield 2 > Wolf: ET, no way. Battlefield 2 is nowhere near as good as ET, even though ET is free.
To the OP, many people like to make open source games, pretty much because they can. The vast majority will be put up on SourceForge.net. GL in your search.