There's a stickied thread containing lists of
free MMO's, some of which are probably FPSes. As for free FPSes which are not MMO's, many exist. A couple that I can think of off the top of my head are
OpenArena,
Urban Terror,
World of Padman (the main site of which appears to be down ATM), and
Warsow.
Honestly, though, if you really want to play an FPS, cough up the $10 for
TF2 next time it goes on sale. It's a little odd at first, but once you get a feel for the game dynamic, it's great fun.
--- Mr. DOS