Coop Games like We Were Here? (or something else)

I am going to go with the very obvious Keep talking and nobody explodes. Other than that no idea, I would be very interested in some as well.

Couch:
Horror: Resident evil 5 and 6 are not the best RE games, but fun in couch coop, Salt and Sanctuary (dark souls in 2d)
Puzzle: Trine 1 or 2, Lara Croft and the Guardian of Light, Portal 2, BattleBlock Theater
Stealthy: Monaco: What's Yours Is Mine

favs in other genres:
Divinity original sin (best case u live with your coop partner ...long game)
Overcooked (nice short fun)
Dungeon Defenders

I don't really have specific game recommendations, but http://www.co-optimus.com/games.php is very useful to find coop games, with plenty of filters and settings to specify what you want.

An obvious suggestion, but there is a sequel called We Were Here Too.

Speed Runners is also fun with friends, different kind of couch game :D

Here are some games that I recommend, some of them were mentioned by other people.

Online + Couch
Ibb & Obb - Platform puzzler that requires strong cooperation
Lovers in a Dangerous Spacetime - Action shooter that requires multitasking

Couch coop only
Lara Croft and the Guardian of Light - Great puzzles, a lot of action, cooperation is the only way through
Towerfall Ascension - Great arrow-shooter platformer with coop and versus
Any LEGO game - Funny content, great gameplay
Jackbox Party - Great selection of games, can also be played on stream
Child of Light - Asymmetrical coop in an otherwise single player RPG
Overcooked - Super challenging levels that require good management and coordination

Blind Trust is a game in the same way as We Were Here which relies on talking things out with a partner, one of you is blind, the other deaf. It's shorter and a bit worse, but it's an unique experience at least.

I'll only list the games that I recall having played or plan on playing with a friend on steam, both out of laziness and readability.
There are probably some more games in their respective series that also allow co-op, but you'll figure that out when you're interested.

By no means do I recommend all of them, but tastes differ, so hopefully someone finds something fun:
(sorry for the length... and yes, I realize I may have had better things to do)

3089 -- Futuristic Action RPG (honestly did not enjoy this one, beware)
Age of Empires II: HD Edition (no co-op campaign)
Age of Empires III: Complete Collection (no co-op campaign)
Alien Breed: Impact
Borderlands
Borderlands 2
Castle Crashers
Clandestine (pleasantly surprised by this one)
Company of Heroes (no co-op campaign)
Company of Heroes 2 (no co-op campaign)
Dark Souls: Prepare to die (not 100% co-op-able, but 95% was good enough, I do recommend Wulf's DSCM though)
Dark Souls 3 (same as above, but ton's easier to coop, no extra's required)
Dead Rising 2 (+ Off the Record)
Dead Rising 3
Elite Dangerous (no co-op campaign, more MMO-ish, but you can party up if that counts)
Executive Assault (no co-op campaign, beware disappointment)
E.Y.E: Divine Cybermancy
Far Cry 3 (technically co-op campaign, but not the main game campaign story)
F.E.A.R. 3
The First Templar
FORCED
God Mode
Half Dead (no co-op campaign)
Hammerwatch
ibb & obb
The Incredible Adventures of Van Helsing: Final Cut
Iron Grip: Warlord (fun concept, but I cannot recommend this one)
Kingdom Wars 2: Battles (no co-op campaign)
Lara Croft and the Guardian of Light
Lara Croft and the Temple of Osiris
The Lord of the Rings: War in the North
Magicka
Magicka 2
Mercenary Kings
Nioh: Complete Edition (also not 100% co-op-able, but close enough)
Outland
Painkiller Hell & Damnation
Particula (not too many co-op tower defends, but still cannot recommend this one)
Payday: The Heist
Payday 2
Planetary Annihilation (no co-op campaign)
Polarity (no co-op campaign)
Portal 2
Resident Evil 5
Resident Evil 6
Rise of Nations: Extended Edition (no co-op campaign)
Saints Row: The Third
Saints Row IV
Salt
Sanctum
Sanctum 2
Scourge: Outbreak
Serious Sam 3: BFE
Shadow Warrior 2
Sid Meier's Civilization V (no co-op campaign)
Sniper Elite V2
Sniper Elite 3
Space Farmers (don't ask)
Starbound
Terraria
Titan Quest Anniversary Edition
Torchlight 2
Total War: Shogun 2
Trine
Trine 2
Two Worlds: Epic Edition (beware of connection issues though, we had to continue solo after we got tired of lag and disconnects)
Two Worlds II
Unepic (not main game campaign, but still fun separate co-op campaign)
Victor Vran
Viscera Cleanup Detail: Shadow Warrior
Warhammer: End Times - Vermintide

Other than these I've played some random other not-really-coop-but-you-can-do-it-with-multiple-people kinda games, like hidden object games (with screenshare if need be), games like little alchemy (online doodle god thing), mmo's, games like Neverwinter Nights 2 or just games like Hearthstone.