Not necessarily in this order but here goes... -Doom 1 & 2 -Half-Life 1 & 2 -Deus Ex & Deus Ex Invisible War -Fallout NV(Would of said 3, but the iron sights sold NV for me) -Duke Nukem 3D -Call of Duty 4 Modern Warfare -Bioshock Too many I can think of to try and limit a list to 10. Off the top of my head though, I'll say these.
I wouldn't classify the Deus Ex games as an FPS, they had more RPG elements than FPS elements. Shooting a gun from a first person perspective doesn't classify a game as an FPS on it's own. Fallout NV was awful compared to Fallout 3 in terms of story and immersion; sure, it had iron sights, but that wasn't enough to make the game more compelling. If all you care about is shooting stuff in a Fallout game, then NV is the way to go, but the story is pretty bland.
Curious, what else is needed for you to count it as a FPS? As that is pretty much what I instantly call a FPS. Also... 1. Half-life 2. Doom 2 3. Half-life 2 4. Halo 5. Duke Nukem 3D 6. Team-Fortress Classic 7. Quake 2 8. Blood 9. Halo 3 10. Medal Of Honor : Frontline (ps2) - That opening D-day level alone get's it on this list. Mind is foggy of FPSs!
You don't shoot anything except portals, to me an FPS would actually be action-oriented, while Portal is a puzzle game that happens to be first person.
In no particular order: Armed and Dangerous Doom 1-2 Halo 1-2 Quake Duke Nukem 3D Castle Wolfenstein Unreal series TF2