Alien Breed 3D
Alien Breed 3D II: killing grounds
Breathless
Genetic Species
Gloom Deluxe

Honorably mentions: Hired Guns

Z.A.R (Zone of Artificial Resources)

Played it some 2-3 years ago. I don't know why, but it captivated me. Too bad the mission pack was only released in Russia, but had a blast with the main game. It was pretty challenging (no saves in a level) and had destructible terrain and interesting missions. The maps were quite small though and they looped around when you went too far in one direction.

What surprised me the most though; it is on Seam :O. I was like WTF, how did it get there and how it's not on GOG.

Super Noah's Ark 3D.

My favorite is Clive Barker's Jericho, superb story and characters. I really recommend it if you like horror stories however the ending feels rushed and it's quite dissapointing.

Seconded. Source port here: https://alephone.lhowon.org/
I second Gunman Chronicles, built on Half-Life it's biggest fail was too be "built on Half-Life". It's a really fun shooter.

Chasm The Rift had a lot of cool ideas, but IMO the game itself really sucks.
LOL Good game though. Should be here (and where the hell are Heretic/HeXen?!)

Hey. We older players used to jump over, duck under, walk around, or simply outrun the incoming bullets of historical weapons.

It doesn't get too much more obscure than Lethal Tender. What a terrible game.

Chasm: The Rift was the first FPS I ever played that had cutscenes.

The game takes place in an alternative reality where the PPSH is manufactured with a lower rate of fire :)

But it has a nice feature: You can´t hurt the enemies until they notice you. Why don´t modern games have this gimmick? Sniper players would love this :)

Probably why airplanes don't fly right in many flight sims, where they also give high gun counts: IRL aircraft cannons are like this gun: it doesn't take long to completely run out of ammo, effectively damaging the usefulness of the weapon. Shooting games don't have you blasting through doors and have pixel perfect collision detection, so it makes less sense for a gun to fire so fast and run out of ammo so quickly. Especially with full autos, people like to spray and pray in video games, which helps the logic of the game: the sniper > full auto > semi auto > sniper balance triangle.

Not my favorite but i remember a good one playing "You Are Empty"

A lot of repeated names for such obscure games. Or maybe goggers all just have very similar tastes :D.

One FPS that I really enjoyed more recent than some mentioned here, and probably counts as obscure- now more than ever, with its name being mixed up with a different game with the same name- is Bedlam.

Fun action, great story and voice acting, and a lot of cool gameplay ideas (the game essentially went through all the famous genres/settings of FPSes and other games level-wise), the only negative point I had when I played it was that sometimes the goal wasn't too obvious, so there was a bit of confused roaming about. I played through it while it was in early access though, and I don't know if something changed when it was released properly or if other people just have wildly different taste from me, but the general consensus on steam is now mixed.

One obscure FPS I enjoyed was Pariah

Also adding one more I remembered. It's more of a racing/FPS hybrid but nonetheless:

Axelerator
Racing from the first person perspective where you can mount guns and destroy other racers.

And regarding Z.A.R
I forgot to mention that it also has a mission pack that was only released in Russia. Not even Steam has that mission pack, so it is probably lost to time. ISOzone has it though (the only one I could find).