Good First Person Shooter/ Third Person Shooter with CO-OP/Online

If you are looking for a great story I recommend you Darkness II or Max Payne 3. You would love it :)

Metro 2033

I would recommend Serious Sam TFE, TSE and BFE. They all have so much gameplay in the main story. You can also play them in upto 16 player co-op which is so much fun with a fair challenge! And oh, they're quite cheap ;).

If you don't bother that it's old, I think System Shock 2 has multiplayer. A very tense game. It's not a pure shooter though.

Call of Juarez Gunslinger - Far Cry® 3 Blood Dragon if you already tried Far Cry 3

it has no coop but i enjoyed it so much

Ghost Recon future soldier

Arma 3

Sniper Elite: Nazi Zombie Army
Sniper Elite: Nazi Zombie Army 2

Half Life series, Crysis 1, Crysis 2

Far Cry 3...never play a game so good ...never play a survival game wich not include zombies...Ubi made a great game ... I recomend u...Has a great Co-op story wich can be play by 4 players...the co-op it's defferent from single player story...but it's great.

I have to say Max Payne 3.. it's an amazing 3rd person shooter and it also has multiplayer

Defiance. There was a sale on steam not long ago. Got it for about 3 pounds and have played around 80h. Pretty decent.

F.E.A.R. Online

Far cry 3, Payday The Heist and Borderlands 2.

CS ftw

Portal 2, not a shooter per se but first person and great in co-op. And once you're finished w/ the campaign there's endless community levels.