GoldenEye 007 as guessed by Entropio
The highest placed first-person shooter on the list is placed this high for a reason. 'GoldenEye' was of course groundbreaking and it is without a doubt the shooter which I had the most fun with. Sure, time took it's toll on this game, but when judging a personal list of "Greatest Games of All-time", the 'fun-factor' is a big piece of the pie. Usually, games based on movies are terrible, but among them, there's at least one that shines high.
The game consists of a list of levels each with a couple of objectives following the events of the movie, but taking liberties where it helps the gameplay and pacing. The development team took many, and clearly had fun in their process. They even modeled the faces of the enemies after themselves! The single-player mode takes plenty of time to complete, but the game also includes an amazing multiplayer. This influential mode puts players against each other in a death match in levels based on both GoldenEye as well as other Bond movies.
For the single-player, the game also included the public secret of the cheat codes. Unlike your usual cheat code, most of these were of little real help to the player, but they were fun additions instead like having every character having a big head and long ape-like arms like Donkey Kong or every weapon shooting paintballs. My parents used to make me use the paintball cheat, because the reddish stains were obviously too much to see for my young self.