What is the steam game that have the best multiplayer and coope mode??

Dungeon Defenders, Sanctum 2 and Orcs Must Die 2. Though for Dungeon Defenders, I will have to warn you to only play with friends you know. Everyone else are terrible people who would screw you over, like ask builders to build defenses, and then kick them when it's all set up.

For classic controlled-chaos co-op, there's the Serious Sam games, along with the Doom Classic series, Quake 1/2 and Heretic/Hexen trilogy. You might want a more modern source port for then though. Serious Sam doesn't have ports, but they have modern remakes called Serious Sam HD, and a modernized version for the classics on the way, but Doom has Zandronum, Quake 1 has Darkplaces, Quake 2 has KMQuake2, Heretic and Hexen can also be run with Zandronum, but Hexen II uses either Hammer of Thyrion or uQe Hexen II.

Payday:The Heist and Payday 2 has the best co-op features.

Loadout is really fun, not techically out yet but you can buy your way into the Beta. It's kinda TF2-esque but you can design your own guns to use, and pick up others' when you kill them.

UnEpic is kinda nice. Mercenary Kings is a good game too.