I don't really have any order to these, I have never been able to claim any game was my "favorite", but these are probably my top 10 FPS games
1. Half-Life series, for obvious reasons
2. Medal of Honor Allied Assault-purely based on the multiplayer, it wasn't good but it was one of my first experiences with online gaming and I spend hundreds of hours playing it.
3. Counter-Strike-the game I would have played instead of Allied Assault had Counter-strike not been rated M, it was the mid 2000s and my parents wouldn't let me play M games. The few times I played CS, I was hooked.
4. Battlefield 1942, Vietnam, and 2-1942 was the first PC FPS I ever played and it was incredible. I had never played a game with this much content, and when I went online and found 64 player battles, I was hooked. Vietnam was the next game I played and I loved flying the helicopters, and then Battlefield 2 made everything flawless, first FPS I played with an experience/level based unlock system for multiplayer (the thing that made COD4 so popular wasn't a new idea). 64 player battles with jets and helicopters flying over head never gets old. I liked Battlfield 3 as well but Origin held it back and I have given up on the series.
5. Deus Ex, Original and Human Revolution- I liked both games about equally, though for different reasons. Human Revolution was not as good, but it was a lot more fun to play for me.
6. Doom-Haven't disliked a Doom game yet, Doom 3 was good but not great and I personally think Doom 1 is better than Doom 2.
7. Bioshock series-liked them all, Infinite had the most impact on me but loved the first the most and even enjoyed the sequel.
8. Fallout 3 and New Vegas-I like the world of 3 better, but New Vegas is better in literally every other way.
9. Postal 2-this game is interesting in that I love parts of it and the overall idea of it, and also agree with people who think it is garbage. One of the games I like thinking about more than playing really, just the fact that it was shown to the supreme court makes me giggle like a schoolgirl.
10. Payday 2-lots of things I hate about it, and yet I continue to play it as often as I can.
Games that I love but didn't make the list for no real reason:
Crysis (first only), Far Cry 1 and 3, Portal series, Painkiller, Serious Sam series, Day of Defeat: Source, Tribes, Mirrors Edge (regret not putting this in the list)
Dishonorable Mention:
Team Fortress 2-this is a personal opinion but I think TF2 was the greatest game I had ever played. And then they updated it. I don't know where along the line I began to resent it, but I officially gave up on it when the engineer update broke 2fort. Don't care if they have fixed it or whatever, I liked the balance of power and tactics and nothing short of reverting to the original game will ever being me back to it. Entirely personal opinion but I truly hate the game as it stands now. This game was my personal version of being a Star Wars fan who hated the prequels. Still love the characters and lore, but that just makes me even more angry because I know I cannot stand to play the thing anymore.