Good Multiplayer FPS?

Enemy Territory or killing floor :)

Payday: The Heist maybe.

any battlefield

Renaissance heroes is fun to play. You can unlock and buy ( for a limited period) weapons, cosmetics and powers. I didn't have the feeling it was a pay2win game though.

Well, Ravaged is also a decent game but I have no idea if there still are people on the servers.

Killing Floor is good for me, I hate losing, and thus i prefer playing against AI and in coop. I like Mann Vs Machine in TF2 too, but it's a bit expensive to buy tickets all the time, and it sucks to play without tickets, since noone is playing seriously without tickets (I play on expert)

Killing Floor. That's it.

Killing Floor, Payday, Battlefield 3, and Blacklight: Retribution (my personal favorite).
If you don't mind 3rd person games, I'd recommend Warframe and Ghost Recon Online.

check out LoadOut its like a beefed up gory version of TF2 and most importantly its FUN FACTOR is off the charts

MicroVolts is pretty good.

and no you dont unlock things in CSGo except achievements and trading cards

Warframe :3

I would recommend these:
Bad Company 2 - for sure far better than Bf3 (I own both, so I say do from my own experience)
Killing Floor - the best co-op game of all time. (Cheap and still gets free updates and events from developers)
Crysis 2 - I still play MP from time to time, definitely more fun than CoD
ORION: Dino Horde - I have reasonable amount of fun for what it's worth, but I would suggest trying it first because many people seem to hate it. (I know I am gonna get trolled for this, but have even bother to play it after all the latest updates? If yes and still don't like it, than simply don't play and move on. But at least developers are actually putting some effort in the game and releasing one patch after another. There is even word about free DLC.)
I would think of more, but I am lazy. :D

Battlefield: Bad Company 2

Halo franchise. the multiplayer is really fun. and they all sorts of game modes you can choose from. I think in Halo Reach and Halo 4 you can gain experience and level up and stuff and unlock new armor to make your dude look cooler. Halo is one of the best shooters ever made. i recommend you try it out. Counter-Strike is a bunch of fun as well.

EDIT: sorry, just now saw you said "on Steam". but if you ever get into console gaming then try out Halo. Good FPS game on steam i would recommend is Counter-Strike series. They always have hundreds of online games going on at any time on any of the CS games.

Arctic Combat, but only in some regions.

Tribes Ascend. Its free to play. You get XP for playing and it varies by how well u do. The XP is used to unlock classes and guns. Lots of hours of fun and its got a good twist to it that no other shooter really does. Check it out.

just played some bnlacklight retribution and it plays great!

I played Gotham City Imposters. Surprisingly great! :D

CS GO. I don't know why you don't like COD. I like MW3 and Black Ops 2. Just brainless run and gun.

Killing Floor is also good.

Counter Strike, any of them.

Borderlands 2

Quake 2 ;D

Battlefield Bad Company 2.

Primal Carnage is pretty good.

BFBC2, though, last time I checked, servers were a ghost town, though, that's for my region anyway. Seriously great game though, I enjoyed it a lot more then BF3, which bores me a lot actually :P