Multiplayer/Coop Games you are looking for [PC]

Portal 2
Never Alone

Some local co-op games I've recently enjoyed playing with my wife:

-Overcooked!
-Lara Croft and the Guardian of Light
-Lara Croft and the Temple of Osiris
-Unravel 2

Saints Row 3 and 4 are great coop games, but for 2 people only. SR3 is a GTA clone with over the top story/humour, SR4 is similar but you have superhero powers.

Borderlands 1 and 2 are great looter shooters with a nice story, they have up to 4 player coop.

Left 4 Dead is a 4-player coop zombie shooter. It's a zombie horde game, you move through maps trying to escape a zombie apocalypse, completeing various tasks along the way. You fight off zombies along the way, defend yourself against hordes, try to manage your ammo and items, etc. It's a lot of fun on the higher difficulties if your friends cooperate well.

Deep Rock Galactic has some replay value.
Styx 2 is great at coop stealth, just like Aragami.

far cry 5, generation zero

Playing Vermintide 2 lately and having a lot of fun. It is one of the best L4D alternatives imo, and even better... it has brutal melee combat.

Try Degrees of Separation, which is a quite good 2-player local cooperative 2D platformer, and can be played alone by switching characters.
Brothers - A Tale of Two Sons is a 2-player local cooperative 3D platformer, which also can be played alone, but the controls are not so great, so find somebody to play with instead (the characters have to be controlled at the same time).
Both games have an interesting story and quite good visuals.
If you are looking for something like Overcooked but with more fun, try Cannibal Cuisine. Note that it's still fresh and has bugs, hope those will be fixed sooner or later.

If you are looking for 4-player party games to play with friends, try these:
Towerfall Ascension
Gang Beasts
Ultimate Chicken Horse
Stick Fight

Sniper Elite has co op campaign
One CoD also has co op campaign (third of one of the series)
Gears 5 has co op campaign
Borderlands has co op campaign
Dying Light has co op campaign
Resident Evil 5 has co op campaign

Yeap, I am all about co op campaign

Deep rock galactic. Upto 4 player co op.
You are doing yourself a disservice if you don't try it out. Amazing game.

Also if you like tabletop games, try FOR THE KING.

Some of my favs along with Dead by Daylight
-Quake and Unreal Tournament Series
-Left 4 Dead 1 & 2
-Zombie Army Trilogy
-Warhammer: End Times - Vermintide 1 & 2
-Helldivers
-Resident Evil 5 & 6
-Saints Row 3rd & 4th
-The Division
-Metal Slug Series
-Guns, Gore & Cannoli
-Alien Swarm & Reactive drop

I second the recommendations for Deep Rock Galactic, great game. The Borderlands series, which is rumored to be free on Epic games store soon is also a blast with friends. Chivalry: Medieval Warfare is a melee based combat game with team objective modes, the taunts and voice commands are a riot too. Destiny 2: The progression / gear system has been screwed up with recent updates, but if you're just playing casually the story missions are pretty fun. HELLDIVERS is a top down / twin stick shooter that's really hard but rewarding. Full Metal Furies is another action / rpg / brawler / puzzle game you might enjoy. Natural Selection 2 - FPS / real time strategy game with a bit of a learning curve, but quite enjoyable once you get the hang of it. I was recently gifted Monster Hunter World, an action rpg where you hunt monsters and collect materials to craft new gear and stuff. Only played a few hours, but really enjoying it so far.

i personally play often worms (ultimate mayhem and clan wars)
company of heroes 2
terraria
Borderlands 1, 2 and Pre Sequel ... i preferred the first Borderlands
dont starve togehter
ultimate chicken horse ... (nvm. saw that you own it already)
the older codemasters racing games like racedriver grid, grid 2, grid autosport, dirt 3, dirt showdown
spelunky
castle crashers
move or die
payday 2
road redemtion
stardew valley
Sniper Elite 4
Saints Row 3 & 4
7 Days to die ... i play it casually with friends but i dont like this game
Space Engineers ... also a game that i personally dont like
... well, thats everything i play atm that's possible to play online coop (may not the old codemasters racing games ... or it depends how you play)

99lives (beat'em up style) it's not my kind of game, but I enjoyed a lot play it with friends (and play it alone sucks)

I'm surprised no one has mentioned Human: Fall Flat yet!
One of my favorites is Crypt of the Necrodancer.
Moving Out looks like a lot of fun too, but I haven't played it.

https://store.steampowered.com/app/410320/EARTH_DEFENSE_FORCE_41_The_Shadow_of_New_Despair/
I don't know if there is still people playing but it is one of the best mp I've ever played.

A Way Out is a nice Coop-Game.
If you are into RPGs, I would recommend Divinity: Original Sin (2).