It's a tough call. I'm not sure I can pick just one as "the best in my opinion". I can, however, pick a few "bests" in subsequent subcategories.
Brought the FPS genre into the lime light - Doom. Wolfenstein came before, but Doom really set the standard.
Redefined not only FPS gaming but redefined interactive gaming - Half-Life. Despite what your opinion is of it and it's ilk, this series set (and continues to set) the bar that many (if not most) other FPS developers strive for in terms of quality and narrative design.
Set the current standard of multiplayer FPS gaming - Counter-Strike & Quake III Arena. These two games defined what online and network shooters should be and how well refined they have to be to remain playable. All online shooters, to this day, owe a debt of gratitude to these two games for basically creating online FPS gaming.
Showed how to and set the bar for cross-genre shooters - Metroid Prime & Deus Ex. Like above, these two games really set the standard by which all adventure or RPG shooters should be judged. Games like Mass Effect and Bioshock (the former a 3rd person shooter, but still relevant) owe their very existence to games like Deus Ex and Metroid Prime. The attention to detail, intricate narrative design, and elaborate, emotive level design were concepts truly refined and almost perfected in MP and DE.
Brought the FPS genre into the lime light - Doom. Wolfenstein came before, but Doom really set the standard.
Redefined not only FPS gaming but redefined interactive gaming - Half-Life. Despite what your opinion is of it and it's ilk, this series set (and continues to set) the bar that many (if not most) other FPS developers strive for in terms of quality and narrative design.
Set the current standard of multiplayer FPS gaming - Counter-Strike & Quake III Arena. These two games defined what online and network shooters should be and how well refined they have to be to remain playable. All online shooters, to this day, owe a debt of gratitude to these two games for basically creating online FPS gaming.
Showed how to and set the bar for cross-genre shooters - Metroid Prime & Deus Ex. Like above, these two games really set the standard by which all adventure or RPG shooters should be judged. Games like Mass Effect and Bioshock (the former a 3rd person shooter, but still relevant) owe their very existence to games like Deus Ex and Metroid Prime. The attention to detail, intricate narrative design, and elaborate, emotive level design were concepts truly refined and almost perfected in MP and DE.