I would have to say, the following, in this order:
Wolfenstein: Enemy Territory Its a classic, free, open-source game released in 2003. While the community is largely dead these days, it was a lot of fun back in the heydey. I still pop into populated servers most weeks and play some rounds.
Zombie Panic: Source This is another freebie (Source mod available on Steam) that I've logged a lot of hours in over the years. It is sort of a FPS and Survival Horror hybrid and can be really enjoyable. Most of the stock maps are great, as are some of the community-built ones.
Left 4 Dead 2 To be honest, L4D2 has gotten a little repetitive and the community isn't what it once was, but its still a fun game for some quick rounds.
Counter-strike: Global Offensive I am sort of new to this title, but its been pretty fun so far. The graphics are a lot better than CS 1.6 or CS:S, but the game play is a bit different.
Anyway, those are the few that come to mind.