https://store.steampowered.com/app/1222700/A_Way_Out/

https://store.steampowered.com/app/1426210/It_Takes_Two/

https://store.steampowered.com/app/1225570/Unravel_Two/

https://store.steampowered.com/app/253230/A_Hat_in_Time/

https://store.steampowered.com/app/620/Portal_2/

https://store.steampowered.com/agecheck/app/476600/

https://store.steampowered.com/app/252110/Lovers_in_a_Dangerous_Spacetime/

https://store.steampowered.com/app/274190/Broforce/

https://store.steampowered.com/app/242550/Rayman_Legends/

https://store.steampowered.com/app/584400/Sonic_Mania/

https://store.steampowered.com/app/345180/Victor_Vran_ARPG/

https://store.steampowered.com/app/598550/HUNTDOWN/

https://store.steampowered.com/app/431940/Wildfire/

https://store.steampowered.com/app/360830/YookaLaylee/

https://store.steampowered.com/app/1016180/Terror_of_Hemasaurus/

https://store.steampowered.com/app/399820/Kopanito_AllStars_Soccer/

https://store.steampowered.com/app/61730/Critter_Crunch/

A few that I've played:

20XX and 30XX - Megaman-style roguelites. Built with 2-player co-op in mind (either local or online) - when playing local, the screen space is shared but the screen zooms out when players are far apart (similar to Smash), so you still get about the same amount of view distance.
Hypercharge: Unboxed - FPS Horde Shooter/Tower Defence hybrid. Up to 4 players (local or online) have to defend cores from hordes of enemy toys, with the ability to place defences to make the job easier. It's mostly about the FPS shooter aspect over the tower defence stuff, though.
Streets of Rogue - GTA1-style sandbox roguelite. Up to 4 players (local or online). To describe Streets of Rogue is difficult. It's a very silly sandbox game where you're given a few objectives (usually neutralising folks or getting an item from another group of guys), but there's always many ways to go about things. It's also one of the few games where the 32 playable characters actually play wildly different from eachother (except the red/blue gangters but that's also the joke), and multiplayer adds another level on top of that as you can easily help (or hinder) eachother's Main Objective, as each class has their own goals.
Helldivers - Top-down shooter. Up to 4 players (local and online, at the same time) get dropped into a planet to complete various objectives. There's a lot of mechanics in this game which would probably kill other games (like how friendly fire is mandatory, or how reloading your gun discards the rest of your clip), but the devs (who also made Magicka, just fyi) made it work very well. There's a sequel coming later this year, too.
Sonic Robo Blast 2 - 3D Platformer. Up to 2 players local splitscreen, or 32 online can play together to run through co-op Sonic levels. Also the only game in this list that's completely free (by nature of it being a Sonic fangame).
A Hat in Time - 3D Platformer. Up to 2 players local splitscreen, and 50 online can play together in a platformer which I honestly find a lot more fun than Super Mario Odyssey. Also, Player 2 is an equal to the main hero this time instead of a glorified "little brother mode" - heck, Player 2 can actually trigger cutscenes and stuff without Player 1's involvement at all. Great stuff.
N++ - 2D Precision Platformer. If you've heard of Super Meat Boy, the original N is the game that inspired it. N++ is just a perfected version of N, with a brand new co-op mode with its own unique levels, which now requires two players to flawlessly move their way through levels where even a single slip-up means starting the level again (though that's fine - they're at max only 60 seconds long, but there's over a thousand of them)
Mercenary Kings - Metal Slug meets Monster Hunter. Up to 4 players local or online. Rise up the difficulty ranks by completing missions, upgrading the parts on your very modular guns and don't forget to eat before you go on a hunt- er, mission.
Pretty much the entirety of the side-scrolling beat-em-up genre, including Streets of Rage 4 (4 player local), River City Girls 1&2 (2 player local) and Teenage Mutant Ninja Turtles: Shredder's Revenge (6 player local and online, yes 6). This entire genre is based on local co-op, so just pick a game and dive in.

It Takes Two is a masterpiece for co-op gameplay and is great for casual gameplay. A Way Out was made by the same studio before It Takes Two and it's easy to see where they were able to improve on the experience, but it's also a great game for local co-op.

It Takes Two.

Which reminds me, we really need to finish that game.

How about firing Dolphin emulator and play some gamecube and wii games.

If you and your wife are into D&D-type stuff Divinity Original Sin 2 has local co-op. It's an isometric turn based adventure game. Super fun to play and on sale for about $18 at the moment, I think. I will say, it's a little more involved than some of the more casual games like Stardew, but if you're willing to put in a little time to learn the game it's one of the most rewarding games I've ever played.

My girlfriend and I actually played through the whole thing together!

LEGO games are fantastic

It Takes Two and A Way Out are co-op masterpieces

Not exactly a recommendation (most of what I would have said has been covered below) but, my partner and I use Co-Optimus to find new games to couch play together. Here's a filtered list of PC split-screen and couch co-op games.

https://co-optim.us/1m8Ysft

Hope that helps!

Out of Space is a ton of fun, starts out hard, but stock with it and you can overcome.

Others I've seen mentioned already, but deserves more: Lovers in a Dangerous Spacetime and It Takes Two

We just played It Takes Two. Great variety of gameplay and level styles. Always something to learn, always something new happening, very different environments. Also, good story for husband and wife coop. Great game, I can recommend!

Me and my gf loved playing Divinity: Original Sin 2.

And we're super excited for Balder's Gate 3 made by the same Devs as DOS2. It's just had its release date move forward to Aug 3rd woo!

It Takes Two is co-op masterpiece. It’s mostly a puzzle platformer but changes up the gameplay style every level. Lots of little mini games to get distracted by too. Can’t recommend it enough

Not split screen but my partner and I are really enjoying nine parchments. She's not a gamer at all, but the game on casual difficulty gives just the right amount of challenge for her.

Will y'all stop making me poorer, damnit! 😉

Magicka and Magicka 2 are great! Can't recommend them enough. Both are on sale rn for like $2.50

There's a mod that allows borderlands 2 to be split screen

It's not a split screen game, but it can be CO-OP. My partner and I play For the King (currently 75% off on steam).

Lovers in a Dangerous Spacetime!

Another not split screen but local co-op, up to 4 players.

If you're willing to get just a little technical you can use nucleus co-op (check out the sub-reddit for details) to split screen many, many games.

Not "split screen" but "same screen":

Unraveled 2

Great for couples.

Castle Crashers and Guacamole 1/2, hands down

+1 for it takes two.

There’s also a pretty nice list already in the comments.

I do like a lot Portal 2 but wifey cannot play for too long with me as she becomes impatient. When that’s the case and she just want to watch a story like you would watch a movie, I play A Plague Tales (both of them) and she ends up wanting to know more and finally, crying.

Both Rayman games are really nice

Screencheet. It's the only fair combative experience.

There are a lot of good suggestions here already. I want throw out Escape Academy. Split screen escape room game. My brother and I started playing it and had a blast in just an hour. Not sure about any story because we glossed over it, but we enjoy puzzles a lot.

Edit to include: Cuphead Wildermyth Overcooked 2 Terraria TMNT Shredders Revenge

„Human Fall Flat“ is pretty good. I’ve played it on switch with a bud and we had a good time. Especially the times we broke the level by sheer accident.

Divinity: Original Sin (and it's sequel) are two of my favorites that I played split screen with my wife. They're classic crpgs, so can be a bit slower paced, but both have great stories and are very good about allowing freedom to both people playing

Grim Dawn is pretty great

Much like others, I can't say enough good things about It Takes Two.

The storyline, great! The gameplay, fantastic! The soundtrack, amazing!

That damn book, pissed me off to no end. (you'll understand that if you play it)

I'd put it up there in my top 10 games I've played of all time.

It’s not split screen, but an enjoyable game for two players in the same screen (so couch coop):

https://en.m.wikipedia.org/wiki/Spiritfarer

You play the new “Reaper” and his cat. Collect lost souls, that still have some issues to solve, travel the “in between” spirit world, build a house boat, take care of gardens, make music, etc. The artwork is cute, while the topics of the lost spirits can be unexpected sad. Still a great game to relax!

if you want some chaos; unrailed, overcooked, and plateup are good