My kids and I have loved these:
Coop:
Competitive:
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My kids and I have loved these:
Coop:
Competitive:
I don't see Out of Space on here. It's pretty fun and challenging.
Goat Simulator is silly fun, especially with kids.
Lara Croft and the Temple of Osiris is awesome since it lets you play up to 4 player co-op.
Vicious Attack Llama Apocalypse is a good co-op twin stick shooter.
Phogs
Idk if this is your speed, but my kid and wife and I love playing the Lego games that are based on movies - Star Wars, Indiana Jones, Avengers, etc.
Very couchable and can be challenging if you try to get 100% on each level.
Apologies if I misread the ask!
Golf With Your Friends literally brings my family together
My mandatory Sky: Children of the Light mention.
Lots of exploring and cooperating with irl co-players (E: you'd have to play on different devices, but one could play on a big screen, and the other can join and use their handheld mostly as a controller) and strangers, some puzzles/quests, some mild scary/dangerous parts, lots of lore, incredible graphics and good soundtrack. It's an open ended game (though some features only become available after your first complete run through) and there is an aspect of grinding if you want to get IGC for cosmetics but you're doing it flying through this gorgeous landscape, and there is a daily cap so you can be pretty chill about it, and IAP are pretty easy to avoid (for me anyway) and are never necessary for gameplay.
There are some issues with bugs, and the company growing and decisions clearly being made by shareholders rather then developers, but at this point it is still absolutely worth playing.
Best couch-coop games
-= FLOSS games =-
Fish Fillets NG
Battle for Wesnoth
Minetest (websearch: Minetest Split Screen Howto)
-= 80s/90s arcade games =-
Bubble Bobble (lesser: Snow Bros or Tumblepop)
Heavy Barrel or Calibre .50 (lesser: Midnight Resistance or Ikari Warriors) [all need 8-way rotator joysticks]
Smash TV(is twin-stick, but awesome) or Narc
Rampage
Gunforce
Double Dragon
Bad Dudes v Dragon Ninja
Final Fight
Golden Axe
Sunset Riders or Vendetta
Silkworm
Cabal
Top Gunner
Side Arms
Alien Syndrome
Gauntlet
Damn, I forgot about Smash TV. Idk how much time my friend and I spent on that game as kids
Lots of time!
...And even more after renting Running Man on VHS :P
There were two isometric Tomb Raider games a couple of years back (Guardian of Light and Temple of Osiris which wasn't as good IMO). You could play in single player, but the co-op mode tweaked the puzzles slightly so you'd need to work together to complete them. And as luck would have it they're both on sale. The first is currently a whopping £1.27 on Steam.
If you fancy going even further back, there was a PS2 game called Kuri Kuri Mix by FromSoft. It may looks like it was made for toddlers, but it was surprisingly tough in places. You almost certainly can't buy that any more, but I'm sure and emulator and ROM site will do nicely.
Old Apache Air Assault is neat in coop
Biped is on sale right now: https://store.steampowered.com/app/1071870/biped/
It's very similar to it takes two
What the Golf? is lot of wacky fun. It's not really golf and has like 500 different levels, some wildly creative.
This is single player though?
No supports split screen coop, at least on PC.
Not to be confused with What the Car? That's single player only.
Borderlands and Full Metal Furies spring to mind.
Rock'n'roll racing is a fantastic coop racer. I think it's available in a remaster from blizzard somewhere.
Pampas and selene: the maze of demons seems fun
Don't Starve: Together
On xbox there’s a Teenage Mutant Ninja Turtles game that’s fun for co-op