Red Faction 1 IMHO was one of the best shooters. One of my favorites and has lots of memories in it too.. It had pretty interesting mechanics. Destructible terrain on a scale noone has ever seen before literally able to travel through huge faces of rock and tunnel with explosives or machines. The fact this kind of technology for gaming was there in 2001 was something quite unheard of, and rarely replicated even in games these days without performance issues. It had the feel of a shooter of the time, like half life, but far more fluid and movement oriented much like halo. The game had a lot things that made it unique from a stealth part of the game as that wasn't fully required but made it optional if you failed that part you weren't fully punished for it entirely. It had decent story, decent visuals and a wide array of weaponry that was fun. (Precision rifle anyone?) There also were some points that had multiple ways to go through a level and made it rewarding to go another way because you might've found some extra ammo, a new weapon or even a vehicle in one case in the underwater area. I thoroughly enjoyed it through and through.

Doom. If not for Doom, the FPS genre as we know it would not exist.

My Vote is on the HALO Franchise, its probably one of the most well known of the FPS genre besides the Call of Duty and Ghost Recon games.

But I think HALO (released in late 2001) still stands out as the best turn of the century FPS games, while it didn't have much in the way of destructible terrain (an experimental feature in that time), it DID have a good assortment of weapons and vehicles, good graphics, some complex physics, and an excellent soundtrack, these combined with its simple, mostly on-rails story at the time gave it an interesting blend of 'do what you want' and 'hey get back here' ness to it . On top of that, while it was simple in gaming terms of today..it was effective...very very effective..and that along with a very interesting Story line (something i think is the most UNDER sold and UNDER rated parts of a good game these days) that would later on be heavily expanded by its massive fan base and developers, gave it something a cult starting point, and in gaming culture, a game with an excellent story and lots of lore will have a life of its own really enough to keep it alive long after its time in the sun is gone (there are STILL people that play the original HALO on PC to this day 18 years later, i'm one of them hehe)

The FPS that actually got me into the whole genre was the original Unreal Tournament.

No other FPS I played before that got the feel of the controls so right. Gameplay was fast and simple, and the controls were just so perfectly intuitive. Also, why can't all the mainstream games go back to the instant-respawn model? I can't stand sitting around in a lobby after getting killed, waiting for a timer, or worse, the match to end.

Half Life obviously deserves an honorable mention. IMO, best example of storytelling in the FPS genre. Too bad about the indefinite cliffhanger they left it on.

Serious Sam.

It's action-movie funny, fast-paced, has lots of neat guns, and throws HUGE numbers of enemies at you.

And the mod support was phenomenal.

Timesplitters 1, 2 and Future Perfect.
Another turn-of-the-century, PFS that lets you build maps and have every character and weapon in any era while having a good time stopping this universal threat!
Great story (Future Perfect) and Sgt. Cortez is a Riot and the BEST protag Ever!!
I hope they bring this back soon, and I hope that you will have a great time with it, too, Sanny.
Stay Burnin'! *Time To Split*

The Metro Franchise, though I would say Last Light is the best of the three.

The reason for this is because I value story as much as gameplay, if not more, and the Metro series has a very human, approachable, and understandable storyline. It gets down to the human level, showing you characters with realistic flaws and virtues, and gives you the ultimate choice to decide just how to approach them. Some situations are so easy to resolve with violence that the first thing you want to do is open fire, but a lot of times in the Metro series...Well, it's just a better idea to wait and see in some cases, and in the long run the series narrative is one of humanity, forgiveness, redemption and hope for a better future than what your forefathers made for you. And I love it for that.

Also, the weapons are fun, the creatures are interesting and intimidating, and the damage system for enemies (realistic damage to gear such as shooting a pouch of ammo off of a vest or cracking a gasmask with a headshot) is pretty nice, too. The latest game, Exodus, is also graphically gorgeous for what it is, and plays like a dream.

I would suggest Bioshock.

It had a very interesting story and unique sci-fi twist. The story kept me hooked all the way through and the powerups allowed for interesting re-plays to explore the full range of design they put in.

Far Cry series
Unmitigated mayhem and a fairly free-roam style allowed you to basically go as wild as you want until you felt like progressing the main story.

and I suppose I'll toss in this last one off the top of my head
S.T.A.L.K.E.R.
This series does a fantastic job at ambient sound, Telling a story, and rewarding exploration and taking risks. While the gunplay does leave a bit to be desired it's pretty adequate. The games are further enhanced with mods that make the game almost punishing to play.

Doom 2016. This brought back the classic game play of the FPSes I grew up with (original doom 1&2, Duke Nukem 3D, quake, quake 2) but didn't completely ignore what had been learned over the years. it was the perfect marriage of new and old, combined with an excellent presentation. Amazing visuals, kick-ass music, and a solid first player game/story.

So many great games already listed. I would add three more: Quake, Duke Nukem 3D, and Deus Ex.

Quake really opened the door for 3D FPS games and game modding. Team Fortress started as a Quake mod, for example. I spent many, many hours of my youth playing Quake and some great mods with friends (I had a 3 computer LAN setup).

Duke Nukem 3D was a direct competitor with Quake, and despite using a more aged engine, was still tons of fun and also had an amazing modding community.

Deus Ex was and IMHO still is the best FPS/RPG. Oh, and the conspiracy theories found in the game are still relevant today (not to mention the game was somewhat prophetic).

Of all time.... I think my favorite First Person Shooter had to be Turok: Dinosaur Hunter. The game just had everything right going on in it. The weapons, the atmosphere, the enemies, the playability, the adventure, the dumbfuckery you could get away with, there was all sorts of fun to be had with this game. The weapons went from down to Earth just to just mindblowingly insane - you went from your typical 'just shoot 'em' guns and ended up with a nuclear arsenal, the fusion canon and the chronosceptor being the biggest guns you get.

The level design was amazing, and makes me long for those times all over again, not like today where everything you see has some practical element to it - like houses have a kitchen, a bathroom, a living room, a bedroom and so on and so forth, where as back then, houses just had rooms that didn't necessarily correlate to anything at all. Or there'd be literal labyrinths that you have to navigate through as every corridor serves almost no purpose to the facility you're rummaging through. It gave a sort of surrealistic feel as you moved from spot to spot.

While the regular enemies were just enemies, nothing special about them, bosses and sub bosses were where the game was at. First cinematic experience I've ever had was a a jeep just jumping from over a wall and trying to run and gun me down, IT WAS ABSOLUTELY GREAT - tame by today's standards though.

Then the damn game had the nerve to actually introduce cheats that revved up the playability and replayability to the extreme. This is where the glitches and what have you were in full view and it's where the nonsense began and never ended. There's so many laugh out loud moments that I can't even possibly remember them all at the moment. You'll just have to play and see.

The only problem with the game - the ending. Absolute shit. You kinda just didn't get one. The place of the person you just defeated explodes, and that's it. MEH. I guess they felt that the game was stellar up to that point, and didn't want to work themselves even more to the bone than they already had while working on the game. It's cool though, the sequel Turok 2 is almost about as fun, but more cinematic and improves on the adventure aspects.