What is the best FPS game I own?

Bad Rats
you have 0hours on it, you deserve to be banned from SG

Sleeping Dogs, for me was a very good game.

How about Mass effect ?

Holy hell, the number of untouched games of quality…

If you want FPS, you have Serious Sam sitting right there. Or Borderlands 2. Or BioShock.
If you want an action game/shooter in general, there is also the GTAs, Batman, Fallout 3, Skyrim.

But seriously, your untouched games have so many great ones, it is next to impossible to just tell one. or even one dozen.

If You choose to play a FPS game, I highly recomended "Rage". It's a great mix of modern and old shool shooter.
For other genres - You definitly should give "Alice: Madness Returns" a try.

Of your unplayed ones -
Metro 2033 is very nice

You have both Crysis and Crysis 2. They're good FPS games, maybe you should try them

Play Deus Ex Human Revolution! :D

I'm gonna say Borderlands

I'd recommend Borderlands 2, great shooter with tons of loot, great writing and good story. I have over 90 hours in that game and I have beaten it twice (on normal) but without doing any DLC's yet. And there's still TVHM and UVHM which are basically NG+ modes. You can spend a ton of time enjoying that game.

Fallout 3 and NV are also games I'd recommend. Start with the third one since NV has more weapons and stuff so F3 wouldn't feel so good if you played NV first.

You also have BioShock.

Battlefield bad company 2 is great!

For FPS, the first Farcry would be a good one.

Play more Borderlands :) But there's also a lot of good stuff that you haven't touched yet.

personally I'd say Portal and Portal 2 are the best FPS games you own, but then I'm not an FPS fan :P
they are really good games though, so I do recommend finishing them (in order)

You don't have many actual FPSs (some of the above suggested games are not first person, so not FPSs).

I would recommend Serious Sam. It's quite entertaining.

bioshock infinte !

You never played Insurgency or Bad Company 2? Both are absolutely worth trying.