What are you're favorite 2-Player Co-op/Versus Game on Steam?

Left 4 dead 1+2

Depends who you're playing with.
The LEGO games are pretty fun to spend time in and since most of them have stories that will be known to you, you can get in and out of gameplay with anyone, gamer or not, and have a good time without sitting through a lot of story exposition.
You have LOTR, you should play it, it's briliant.

For more softcore playtime, Portal Knights is also great to play in co-op as well as the Trine games.

For something a little more on the gore side, How to Survive is cool.

For Co-op:
Risk of Rain 2
Overcooked 2

marooners
ticket to ride
super mega baseball

Duck Game <3

crawl
nippon marathon

Last "co-op" I played was Risk of Rain with a friend. Not sure if that counts though.

Here are a few of the ones I have really enjoyed :)

Local coop only

Towerfall Ascension - The versus mode is perfect for 4 players, but the quest is well suited for 2 player play.
Any LEGO game - Well fitted for more casual players
Lara Croft and the Guardian of Light - An asymmetric action-adventure game with various challenges and puzzle tombs

Online coop only

Tower Unite - A VRChat-like universe with minigames, casino, arcade and lots of customization, pretty cool to hang out with friends.
Dead by Daylight - A thrilling game that makes it fun to squad-up with friends to get murdered

Both local and online coop

Ibb & Obb - A beautifully simple coop platform puzzler that takes its concept very far
Farm Together - A nice 3D farming game with tons of customization and that you can easily pour weeks of time in
Stardew Valley - An immersive farming/fishing/adventure world in a cozy town full of upgrades
Rocket League - Soccer with cars, with immersive graphics and sound
It Takes Two - An asymmetric 3D platformer adventure with many levels that make use of cooperation in so many ways
A Hat In Time - Incredibly fun 3D platformer adventure

Both online and local;
Battle Block Theather
Human: Fall Flat
Portal 2

Just local;
Crawl
Ultimate Chicken Horse
Mortal Kombat
Any of the LEGO games

Local co-op:
Biped
Blazing Beaks
Pikuniku (though there aren't many levels for co-op, but I had a lot of fun nevertheless)
Wildfire

Online co-op:
100% Orange Juice
Darksiders Genesis
GTFO
Hellpoint
Human: Fall Flat
Killing Floor 2
Sea of Thieves

Both local & online co-op:
Just Shapes & Beats
Kingdom Two Crowns
Moon Hunters
Overcooked 2
Trine - all of them, except for 3rd
Unrailed!

Online pvp:
100% Orange Juice
Cake Bash
Ultimate Chicken Horse
Witch It

A buddy of mine and I had great fun playing head to head Jedi Knight then Jedi Academy. One of us would host the other, and play 20 minutes/first to 10 points games in a medium-sized map. You want a place big enough to run away when you have to, but not so big you never find each other. There are a bunch of cool user-community-made maps out there, too.