Zefer

You could try tremulous, but it has a steep learning curve so it may be more suitable as a long term interest instead of a short term one. The graphics are of course dated, and the various clients can be somewhat confusing to new players. But, it does run on nearly any computer and it is a small download with a quick install.

There's insurgency, which is a HL2 mod. It has combat that's semi-realistic and can be entertaining at times.

Another HL2 mod is Empires. One player on each team is a commander and plays the match as if it were an RTS. The rest of the players are foot soldiers, carrying out the orders of the commander. Different classes are available to the the player and each has special abilities it can use.

There's also Wolf Team, but I would only suggest it if you're desperate.

I don't know what else I could suggest because the other FPS's I know of that have not been suggested either have too small of a community or aren't good enough for me to ever recommend to anyone. I also have the feeling I played another game worth mentioning, but I just can't remember a name.