Recommend Me A Good First Person Shooter.

team fortress 2, battlefield 3/bad company 2(still has a strong playerbase), borderlands 2

HL2: Episode 3

Deus Ex: Human Revolution, Serious Sam 3: BFE (ignore the story, it's not important), Serious Sam HD (both encounters), Killing Floor, Metro 2033... I can do this all day :)

Payday The Heist!!!!

Wolfenstein: Enemy Territory. Beats all the mentioned above and below.

Dead Island

Start with everything id Software, Epic Games and Valve Software. When you're done come back and you'll get more.
And don't disrespect these games. If it has 3 difficulties, choose the hardest, if it has 4 at least 2nd hardest, if it has 5 al least 2nd hardest.

counter strike you pick which one

Bad company 2 because it's literally 10 times better than BF3 (I AM ALLOWED AN OPINION), Deus ex (first one or human revolution, invisible war wasn't as good), bulletstorm, borderlands, or bioshock.

Arma2 for realism

HALO

STALKER

Half-Life franchise, Stalker, Metro 2033, CoD 1, Singularity

Payday.

Deus Ex, Quake, Doom, Bioshock, Half Life series, Team Fortress 2, Section 8, Zeno Clash, PAYDAY: The Heist, Hard Reset, Far Cry, FEAR and some others

I actually found Rage to be quite entertaining.

PAYDAY is also very good. If you haven't played the Half-Lifes, you HAVE to play those.

Tribes: Ascend

for multiplayer: unreal tournament 2004; battlefield 3.
for singleplayer: bioshock; metro 2033; prey is cool, too.
hard reset is also fun =)

Bulletstorm, Hard Reset (hard, old-school fps), Bioshock (story wise, combat system is weak)

Revelations 2012

It would help to know what kind of shooter you are interested in playing. People just randomly shouting out titles doesn't seem like it would help much.

What do you like? What are you into?

Prey, Bioshock 1 & 2, Half-Life 1 & 2, Hard Reset, Metro 2003

Arma 2 combined operations

Postal 2. Really.

Try Firefall