10: F.E.A.R.
While I admittedly know little about this series, the plot seems to be intriguing. To be fair, there are probably several games that tie with this one due to their excellent combination of fps mechanics and horror(possibly Dead Space).
9: Cryostasis: The Sleep of Reason
As previously acknowledged, when the fps genre is successfully blended with survival horror, the resulting product has a high potential to tell a good, creepy, complex, suspenseful, and mysterious, story. This game is a perfect example of said potential game.
Another example of the previously described characteristics.
7:Fallout: New Vegas
New Vegas offers an fps experience in the RPG world.
6:Call of Juarez
While Billy's campaign doesn't deliver as well as Ray's, this game would make an excellent western movie.
5:Deus Ex
The ability to access the same situations in different ways puts a positive spin on this game's story elements, and adds to its replay value as well.
4:BioShock
Another excellent horror/suspense-fps
3:Half-Life
While this game's plot isn't entirely original, it was blended with its gameplay in such a way that makes it very engaging, interesting, and seemingly original.
2:Call of Juarez: Bound in Blood
This game took all the western cliches that made the first game great and made them better. Bound in Blood does a very efficient and clever job of explaining what happened before the events of the first game; it explains connections between characters, the significance of seemly meaningless events, and it fills in some blanks that the first game left partially empty.
1:Golden Eye 007
The game is bond, James Bond. If you don't understand that, buy the game, play it, and understand why it's better than almost(if not) all modern fps games.