Highly recommend Shock Troopers if you've never played that

Windjammers too actually, but I guess that one's still competitive? I'm not sure what the criteria is.
Undercover Cops is another great one, too.

@rapid_progres this list used to be private but I wanted to share it with a friend so I made it public without giving much context as to what it's about but you nailed it with those suggestions, thanks! Basically any coop game available in fightcade that's not a fighting game.

Although not strictly fightcade, for fighting games I have this:
https://backloggd.com/u/mutyumu/list/fighting-games-i-want-to-try/
https://backloggd.com/u/mutyumu/list/favorite-fighting-games/

small update: I started playing Contra with my friend and there were desync issues starting on Stage 3 so that was a bummer :(

they consistently happened on stage 3... not sure if it's because we are too far (I'm in the UK and he's in the US) but then it's weird it always happens on this stage so I want to try other emulators/games (next will be Metal Slug probably)

^NES Contra