We never had a PC in the 90s/00's so I never got to play pc games until 2009 at the earliest
What are some of the essentials that I've missed out on, currently have played/completed
Duke Nukem 3D
Blood
Doom
Hexen
Return To Castle Wolfenstein
Currently playing pic related and having a blast
Serious Sam : The First(/Second) Encounter are pretty good games.
HD remakes are good but remove some content like altered gravity rooms etc.
Shadow warrior is great
also don't skip out on mods.
Heretic is really good.
Hexen 2 and Heretic 2 are also pretty solid. They depart a bit from their predecessors but they hold their own.
Perhaps only technically "FPS" by the literal definition of first person shooter, but Descent 1 and 2 are both good games.
Dunno if you want to try mods/total conversions but doom and quake are full of that.
You can add powerslave (the game was different for each console+pc and the current remaster on steam is a melting pot of all)
I can also suggest rise of the triad(if you can stomach a wolfenstain clone), but wait the new steam release.
warcraft2
lucasarts DOS adventure games, monkey island, sam max, day of the tentacle
dune2000
command and conquer (redalert)
netstorm
Soldier of Fortune and SiN are both great, I would also recommend Soldier of Fortune 2 albeit it's much more grounded than its predecessor, the multiplayer for 2 was awesome back in the day, wasted countless hours on it.
Deus Ex and System Shock 2 are must plays.
No one lives Forever is also really good.
Unreal Tournament 99 and 2004 - those are multiplayer games but have very well behaving bots. Unreal can be a bit boring to play through (wouldn't recommend hard since enemies tend to be spongy - I can only suspect it was intentional to make the game harder but also showcase all the animations and AI behaviour)
F.E.A.R is one of the best shooters ever made. Sadly, everything after the main game dropped the ball to a varying degree.
Aliens vs Predator 1 & 2 (haven't played the first but I absolutely love 2, sadly it can be hard to get running on a modern OS).
HL, HL: Opposing Force, HL2 are great, with the Episodes being worthwhile as well.
If you don't mind the hybrid gameplay, Deus Ex and System Shock 2 are some of the best games ever made (the latter has received a number of patches/mods that improve the experience in a faithful way - https://www.systemshock.org/index.php?topic=4447.0 . DO NOT USE REBIRTH MOD, IT IS A FRICKING ABOMINATION. I'd limit myself to SCP, SHTUP and Vintage Song Remake).
S.T.A.L.K.E.R is another great game but needs some time investment (OG doesn't pick up until 2nd-3rd zone but when it does, it gets phenomenal. Clear Sky is a bit harsher in that regard).
Try Metadoom, it's epic
Unreal Gold (not tournament) if you want a classic sp experience.
Essential? Definitely deus ex.
The first System Shock blows the second one out of the water, but it leans more towards dungeon crawler than first person shooter.
Painkiller: Black Edition
Far Cry 1/2
Crysis
Prey (2006)
TimeShift
No on lives forever 1 & 2 OP
Descent
Half-Life 1-2 and expansion packs.
FEAR + expansion packs.
Far Cry 1.
Crysis 1 + WH.
STALKER:SoC, CS, CoP.
Quake 2 and 4.
Riddick: Butcher's bay
Unreal
SWAT 3 and 4
Max Payne 1-2; not FPS, but close enough.
If you bring up Max Payne then you have to add the rest of TPS games like RE4, GoW etc.
I will never consider RE4 an TPS. It's a beast of its own. GoW was always meh as frick. I played the first three with a buddy on his Xboxes.
There was fricktons of far better TPS games back in the 1990s and early 00s.
If Quake ends up leaving you feeling a little empty or just wishing it had a little more substance, I highly recommend checking out the Arcane Dimensions mod. It's Quake with some beautiful levels, new enemy types, new weapons make an appearance and some fine-tune adjustments.
Also I hope you're playing through the main game with the soundtrack enabled.
Seconding Arcane Dimensions and the rest of the Quake mods. Brilliant stuff, all of them. I only wish someone had the acumen to string together a proper campaign like the main game and its expansions, but oh well.
Dark Forces 1 and 2
My childhood was growing on Duke Nukem 3D and Shadow Warrior and Duke was one of my favorite games of all time. Then I played Blood (1997) and I was mindblown how much better it is. It's unique with a gameplay flow that is unlike another, I have not played an FPS that would rival Blood yet. And frick games like Cultic, they are just poor imitations.
Gunman Chronicles
Star Wars: Dark Forces is incredible.
Im still playing Quake Champions. Im still here but where the hell are you?
All old Valve games (Half-Life etc.)
Deus Ex 1
XIII (classic)
Fahrenheit: Indigo Prophecy
Old GTA games
Far Cry 1 (beware, it's very hard game)
Vivisector: Beast Within (it's abandonware, so you have to use google to find the download link)
Most of the stuff already said in the thread is genuinely great however...
Valve titles are overrated to hell and back and that's ignoring the mods which are almost always included when people talk about them
but I'll have to pick serious sam
https://alephone.lhowon.org/
Play the other ravensoft games like hexen 2 and heretic.
Heretic 2 if you can find it somewhere.
If you liked Duke 3D give Alien Armageddon a try. Some of the best modders in the Duke community made it.