1. Half-Life.
2. Half-Life 2
3. Goldeneye 64
4. Timesplitters 2
5. Call Of Duty 4

Oh my bad I thought you were asking what it was called on playstation....

1. Perfect Dark (N64)
2. Goldeneye (N64)
3. Halo 2 (Xbox)
4. Doom II (PC)

And I'll throw in something a little different for number 5.

5. XIII (GC)

As much as I'd like to come up with five of the best FPS games ever, I cannot extend the list past #1. I am a huge Zelda fan but there is not a single Zelda game that can compare with this. I consider this the single greatest game ever (except for Tetris Attack (maybe)).

This game single-handedly changed how I look at and play games. This is the game that changed video games from a hobby to a sport for me. I can attribute my current lack of interest in long games (20+ hours) to this title. This game changed gaming so that I play in short 15-20 minute sessions and each time get better. No more rigorous 60 campaigns to finally "beat" the game. You sat down, played, got better, walked away and did it again later.

Quake III Arena (PC)

Load this game up and get into the online community in 1v1, TDM, and CTF and you will find the ultimate game. So many mods made for that game simply rocked. (OSP, Freeze Tag and CPM are the best) Going to Quakecon for a four day gaming party totally rocked both times I went (2002 and 2003).

I used to love console gaming from 1989 all the way through 2000. It was in the end of 2000 that I really picked up Q3 and console gaming just isn't the same anymore. I have so many games that I haven't finished because I just get bored of them. I want to sit down for an hour and play three or four full games and improve my skill and then quit until next time.

Quake II Arena is the single greatest game ever, let alone FPS, and I cannot even think of tarnishing it by including a number two through five. They simply don't exist. Not once you play this game in the truest sense.

Half Life 2
Timesplitters 2
Call of Duty 4
Timesplitters Future Perfect
Medal of Honour Frontlines

I've certainly enjoyed numerous FPS games, but I'd say that games pumped out by Valve are usually some of the better ones I've played.

Half-Life
Half-Life 2 (and episodes)
Team Fortress Classic and TF2
Counter-Strike (1.6, CZ, and Source)

I'd have to say that these are some of my favorite games that still get playtime to this day. I never really got into Day of Defeat, but I do play Day of Defeat: Source from time to time.

There are other ones which are good too,

The Battlefield series (I own and still play BF2 from time to time, it can be good even though it has a lot of issues).
Bioshock - It was good even if I didn't like the level progression (oops, this area is now blocked..... go around and do a bunch of crap to unblock it)
Call of Duty 4 - Short and very linear, but it had some cool moments that are fun to replay.

1. Half-Life/Counter-Strike
2. Turok:Dinosaur Hunter
3. Bioshock
4. Goldeneye
5. Doom

1. Counter-Strike 1.3 (bring back bunny hop)
2. CoD4(PC)
3. CoD
4. Resistance 2(only console on the list)
5. Rainbow 6: Athena Sword

yes 1.3 was best!

I miss the older Warcraft 3 servers (the ones now have way too many classes, items, ect). I loved playing an undead with the faster running speed and lower gravity jumps. Snaking around objects while jumping was great.