Doom 2 - first FPS I've ever played, plus you had the BFG
Duke Nukem 3D, just loads of fun, RPGs
Quake - fun and you had mods + skinz
Tribes - vehicles, jetpacks, classes, open terrain, team play, mortars!
Half-Life I - great story and game play
Well, historically, I'd say (defining top-ness as major innovation):
Wolfenstien -- (Father of the FPS)
Doom -- (Mother of all FPS...es?)
Quake -- (Polygons and 3D acceleration for the FPS)
Tribes -- (online team FPS)
Counterstrike -- (yes, it's just a Half Life mod, but still...)
My personal top five has more than five!
Doom/Doom II -- (Who can forget all the PWAD fun! YakWorld! Yay!)
Duke Nukem 3D -- ("Shake it, baby!" 'nuff said! )
Half Life -- (immersive. I still play the tram-ride over and over!)
Unreal -- (It was just so PURTY and the levels were so BIG, and the sounds were so good and the music was neat!)
Unreal Tournament -- (same as Unreal, but with tight online gameplay and great bots!)
Call of Duty, single player game. -- (Since my Dad was a Marine in the Pacific Theatre of WW-II {2 Purple Hearts and a Silver Star, and grenade shrapnel in his eye, from Saipan}, I've always had an interest in all things WW-II related.)
Shocked and appalled that I forgot about Operation Flashpoint.
Once I got that game it pretty much took precedence over any other military shooter in my collection, for like 6 years. The mission editor is really where that game shines, easy to use even for a novice and easy to become better than a novice at mission making using it. This is what kept its appeal for me along with the unending influx of mods and addons. I probably made like 15 full length campaigns for the game, based on my own invented Ideas for fictional wars. It was just so versatile. I always liked having missions, involving helo extractions/insertions under fire.
Arma was ok, basically flashpoint with a little better graphics. Looking forward to OFP2. The only aspect I though was lacking in OFP, was since they were going with such realism from the aspect of the squad/infantry level, though you can also drive all the vehicles and its fine when you arent in a vehicle, I wish they would put more effort in the vehicle simulations. i.e. if you played M1 tank platoon 2 (unfortunate there was never a worthy 3rd installment) and then commanded a tank in OFP you would see what I mean.
Online play essential for a good FPS in my opinion
Rogue Spear (Never looked back at RTS after finding this game)
Return to Castle Wolfenstein (particularly once you include enemy territory)
Call of Duty 2 (Smooth)
Battlefield 1942 (Huge - later versions all disappointing)
Duke Nukem 3d ("Suck it down" this game and a large bag of jelly babies each week was responsible for me having very pale skin and large eyes as a teenager)
If I had a £1 for every hour spent playing the above 5 games I would not have to work for a very long time (actually I just worked it out and I reckon 20 hours a week, every week for 15 years so about £15,000 so maybe I wouldn't exactly be able to retire but it is still a lot.)
Non FPS though, and I may be showing my age, you would have to go a long way to convince me that Tie Fighter wasn't a gift from heaven - makes me cry to try and play it now though - the graphics all looked so good back then.