I've played quite a bit of FPS titles. Some of my favourites are (excluding games like Fallout and Deus Ex, which are more RPG-ey):
* Call of Duty 4: Modern Warfare: Basically the game that reinvented the modern FPS genre. Singleplayer campaign is great, too.
* Call of Duty: Modern Warfare 2: Still the pinnacle of arcade-y modern FPS. Its fast pacing and precise gameplay (hooray for hitscans) + tons of weapons, perks and customizations make it enjoyable for eternal play (I've spent more than 2200 hours on the multiplayer). SP campaign is great.
* Far Cry 4: It expands FC3 far and beyond. Mechanics are great (par with MW's), multitude of guns and tactics. ANIMAL FIGHTING YEAAA! Too bad the coop mode is buggy 🙁
* Insurgency: One of the best coop games I've played. Too bad devs still use Source engine, which is very limited compared to any modern 3d engine. Still receives updates from devs, which is awesome.
* Call of Juarez: Bound in Blood: Wild West is one of my favourite themes (alongside with Prohibition/Sicilian Mafia). Nicely executed, even though there are some plot holes.
* Call of Juarez: Gunslinger: They simplified some of the mechanics to offer a more straightforward experience. Really cool plot. Gorgeous art and good graphics. The only bad thing is that they didn't implement multiplayer, which would be great.
* Bioshock (series): I must be one of the few people that like the 2nd chapter better than the first. Infinity is on another level of awesomeness. If you have not played it and crave for nice plots, do not waste another minute.
* STALKER (series): Awesome immersion. Bad engine. Loads of guns. All for all, good games.
* Crysis (and Warhead): If you put the whole resource hog apart it's a pretty solid shooter with cool mechanics and very large maps. Really fun to play.
* Postal 2: Dumb fun.
* Call of Duty 1/2: Great for their time as it added the "real war" feeling with comrades that fought alongside you (enve though they sucked most of the time and couldn't hit anything, hahaha)
And some of the games I can't play at all (because either horribad or didn't feel right at all):
* Doom 3: The departure from the tried and true run'n'gun formula from the previous titles was too much to bear.
* ARMA Series: Way too much simulator into it. Spending 15 minutes walking on a forest and firing a rifle with a 1x Red Dot sight at enemies at 300 meters isn't slightly my definition of having fun.
* Call of Duty: Ghosts: Should I say anything more? Uninspired, boring, repetitive, etc.
* Call of Duty: Modern Warfare 3: My biggest disappointment in gaming, ever. Was so hyped I pre-ordered it. After half hour on singleplayer I knew instantly that the MP portion was ruined, too. 🙁
* Painkiller: Very repetitive. And by that I mean really, really repetitive.
* Serious Sam: Same as above. A bit more repetitive, though.
* Call of Juarez: The Cartel: EVERYTHING WAS WRONG