Yes, another "best..." thread. Topic says it all.
Personally, I think Crysis has to be the top choice for me. I bought it for cheap during the steam sale and I've played it more than any of the other (many) games I bought last month. There's such an amazing sense of freedom in the game. Also, I've never played a game that made me feel like such a pure badass. With the powers, it's like a first-person superhero game. Many gamers complain that its just a graphics showcase with two-dimensional gameplay, but i actually enjoy the gameplay more than the graphics.

Dark Forces, one of the best star wars games ever and one of the few where you don't play a jedi

Hexen.

Tribes and Tribes 2

I'm still going to have to say Mirror's Edge.
While not a strictly a Shooter, it's still the most enjoyable first person perspective game I've played.

STALKER is a strong contender. Especially with a few mods (not Oblivion Lost). Half Life is another.

Mine is definitely Half-Life.
Though I don't play shooters too much and propably haven't played anything younger than Far Cry.

The Ultimate Doom.
I can never tire of coming back to it.

+1
A very innovative FPS (or should I say "Doom-like", as it was the usual term back there) for its time, and an excellent Star Wars title, very immersive.
And you said it, the character you played was not a jedi (yet...), it's one good point for me in a SW game, now you always play jedi... Surely because of that I liked Republic Commando and Bounty Hunter.

The original Quake. A modding toolkit/ toybox bundled with a great example FPS.

No One Lives Forever 2?
Purely based on retro, spy mock, cool.

It's a cliche, but my favorite first-person shooter is still Deus Ex.
My favorite first-person game is Thief 2.

Purely FPS, I'll say the Serious Sam series.

Thirded. This is probably one of the few games from that era from which I can still picture the levels in my head. The dark troopers were scary back then