My favorite free shooter is America's Army:
It's a game developed by the U.S. Army and is used for recruitment. You basically go through a bunch of training missions, and then you play online team vs. team style similar to Counter-Strike with rounds and such. It's uber realistic, a few shots and you're done. You can pick different classes to be (which is where the training comes into play, if you don't have the training, you can't be that class) like medic, sniper, or special forces. It's a lot more tactical than most other online shooters like CS though, there's more waiting involved, grenades play a huge part, and you really have to rely on your teammates.