A couple titles that deserve mention and I don't see in any other lists:

Children of Mora - Narrative driven action RPG with some light Roguelite-ish elements. Amazing world building and story telling, good character choice/building and gameplay.

Cassette Beasts - Pokemon, if it were good. Much more mature story, tons of quality of life systems that makes building things fun, a weakness system that matters a lot more than "number big" and the entire game is double battles. I've played the game start-to-finish in couch co-op and it was incredible. They've recently added online multiplayer, but I cannot say with 100% certainty that the online allows you to engage with the story together. Couch co-op has one player play as the companion character in an otherwise unchanged experience whereas online has one player character hop into another player characters world.

Weird enough, the Monster Hunter franchise - I'm not sure how this isn't anywhere else in this thread. Use large weapon to hunt large monster. Build bigger weapon to hunt bigger monster. World and Rise are both on sale on Steam right now. World is dumb to move through the story together though, despite the fact that most fans who aren't me are likely to call it the better game.

Elden Ring with the Seamless Coop mod looks like great fun if you enjoy that type of game. I've wanted to try it for a long time.

Don’t Starve Together

Pikmin 3

Overcooked

V Rising - 49.2 Hours

• Online Co-op
• Isometric perspective
• Vampire survival/crafting
• Be a vampire lord with a keep, thralls, blood banks, cast magic, wild shape to a wolf, decorate a castle, posess a horse, make your Castlevania/vampire fantasy come true!

Enshrouded - 123.3 Hours

• Online co-op, 3rd person perspective
• Absolutely beautiful and haunting exploration/survival/crafting/action rpg.
• Early access and already has had large updates
• Wonderful and detailed building system. Will post pics if I remember when I'm at my PC.

Remnant II - 22.5 Hours

• Online co-op, 1st/3rd person
• Soulslike shooter
• Has been quite challenging playing it single player but co-op seems like it could be good with easier progression

Stardew Valley - 252.2 Hours

• 2d Pixel graphics
• Online co-op
• Huge game that has had many updates
• Has been $14.99 since 2016 and will always be $14.99 per the one man developer. All DLC is free and included.

Edit to add: 9 Monkeys of Shaolin - 7.0 Hours

• 2.5D Kung Fu ARPG Brawler
• Open skill system is fun
• It's kung fu. I am not familiar enough with Shaolin staff styles to say if the moves are authentic or not.

Unravel 2

for local coop of course portal and as a bonus, kid safe, - it takes two, biped.

Torchlight 2 and 3 are fun looting co-op experiences.

I'm currently playing V Rising right now with my wife after Divinity 2. We are LOVING it. Definitely give it a try!

I’m playing through BG3 with a good friend too, we’re actually planning on doing another, wildly different, playthrough when we’re done with this one. We’re playing sorta chaotic/neutral good right now and intend to do an evil campaign next with different characters and classes and possibly even modded.

Now I obviously haven’t tried it yet but the game has so much hidden stuff, branching paths and different-to-play classes I’m fairly confident you can play it at least twice and have an almost entirely new experience!

I believe the entirety of the Gears of War series has a co op mode

Also if you don't know anything about the series like I did before playing Gears 5 with my kids, don't play it with kids....

Most of these have been mentioned before, but I'll mention them again.

Halo Master Chief Collection. Everything before 5 is local split screen. 5 requires two Xboxs. I would just avoid Infinite, but I believe it also requires two systems, maybe including PC.

Diablo 3 is very accessible. 4 should be as well. I'm told Diablo 2 is the best, so I need to try to get back into it. All should be good options.

Monster Hunter requires more patience. At least for World, cooperation is good but really the game is geared towards individuals being able to take charge as necessary. Track, set traps, bait, capture, etc. Multiplayer is VERY useful during fights though.

Stranger of Paradise is kinda Souls-like but more forgiving. In my experience it's A LOT more friendly to Multiplayer. It's also a ton of fun with a friend.

Psi-Ops: Mindgate Conspiracy. An old PS2 game. One person controls the body, the other controls the mind. Especially if you have a Gameshark and you can go Godmode.

Any of the old Street sports games were a blast back in the day.

Older Twisted Metal for another old-school recommendation.

Assuming Steam?

• Halo, obviously. Master Chief Collection is pretty cheap to pick up these days, don't miss out on the Halo 3 ODST DLC.

• Ready Or Not can be a challenge with just two people, but it is very rewarding to get a good score.

• Zero Hour is very similar to Ready Or Not, but it has different features and I find it a bit easier.

• Deep Rock Galactic

• Risk of Rain 2

• Elden Ring (Seamless Coop Mod is highly recommended)

• Monster Hunter World (include Iceborn DLC)

• Generation Zero

• Project Zomboid (if you like this one you'll probably sink hundreds of hours into it)

• theHunter Call of the Wild (chill hunting shooter)

• Farming Simulator 2019 (new ones may be better, haven't researched)

• Barotrauma

• Factorio

• Elite Dangerous

• Green Hell

• The Forest

• Sons of the Forest

• Morrowind has an OpenMW fork that supports multiplayer, if you get it set up this can be a fun game to play

Gauntlet

Can't believe I hadn't seen anyone mention "it takes two" great game, was free on Gamepass when I last played it.

Subnautica can be played together using the Nitrox mod

https://nitrox.rux.gg/

Rayman Legends.

Grab a PS2 emulator and give Kuri Kuri Mix a go.

It's by FromSoft of all people and it seems hardly anyone has heard of it.

Popping in to suggest Ship of Fools and Cult of the Lamb

Ship of Fools was shorter than I'd like but lots of fun. Currently playing through Cult of the Lamb co-op and and we've been having a blast

If you don’t mind horror games, the entire Dark Pictures Anthology and The Quarry are really fun shared stories with branching paths.

Grounded

If you're into souls-likes, try "Stranger of Paradise"

Its fantastic, nobody has heard of it for some reason. I played this last year with a friend and it was really fun (if you're into that playstyle)

Darksiders Genesis was also very fun with my little cousin, more hack n slash, one player gets to be pure meelee and the other half meelee half twin stick ranged.

Sniper Elite (4?) is pretty good as a chill co op FPS mission progression game.

Otherwise, probably any survival craft will do, you already played a few. I enjoyed Valheim and Planet Crafter and wish Subnautica had Multiplayer.

Nine Parchments - Top down Magic slinging romp. Similar to the Majica series, but with less knowing how to do certain key-press combos.

Orcs Must Die 2 - 3rd person tower defense where you place traps and use spells and weapons to take down foes. Continues the story of the first game, which did not have multiplayer, unfortunately.

Children of Morta - Top down dungeon crawler. Take on the roles of a family trying to hunt down an ancient evil. Like the Belmont's of Castlevania fame.

Full Metal Furies - Top down action fighter. Fight the Titans as some of the last remaining survivors of Ragnarok. Fun dialing with a good-sized world map to explore.

Astroneer - 3rd person survival crafting on a randomized planet. Cute component designs and a unique air management system. Plays best with a mouse & keyboard.

Deep Rock Galactic - Space Dwarves Corporate mining simulator. You and up to 4 friends drive do into infested planetoids in order to make some Gold. Destructible terrain and shenanigans.

Solasta crown of the magister

Steam link

The "We Were Here" series is a fun puzzle co-op game. The first one's free if you want to try before you buy.

Warframe

For crafting/exploration/survival I'd recommend Valheim. Don't judge it by its looks, the game is insanely fun with friends.

It's an old game, but Pixel Junk: Monsters is a ton of fun as a co-op tower defense. Don't bother with the sequel - s'bad.

Unraveled 2 is a beautiful and fun game for 2 people.