I'll list a lot of them, just try them or check on youtube first to see if you like them.
Edit: difficulty based on what I remember when I played them 20 years ago.
Beatm'em All:
TMNT IV ~ Turtle in Time (funny and not too hard. Co-op, you can finish the game in one session without problem)
Casual Plateformer:
Asterix & Obelix
Bubsy
Chuck Rock
Cool spot
Earthworm Jim
Super James Pond II (or 3)
Maybe a little hard for today's specs :
Donkey Kong Country (already mentioned as a hard one, but it was a good one back then. I suggest you try it and make your own decision, that's what game lists are for)
Hook
Indiana Jones Trilogy (greatest adventure)
Inspector Gadget
Tiny toons
Road Runner
Super Adventure Island
More plateform adventure, still enough casual for you?:
Adam's Family (the first one. jump on enemies head like mario)
Plateform Puzzle:
Lost Vinking
less known games:
Go go Ackman (plateformer)
Super Bonk (plateformer)
Harder, not casual/plateformer:
Starwars games (plateformer/Mode-7. very hard)
Jurassic Park (top down action)
Pocky & Rocky (top down action/shooter in Co-op)
Pop n Twinbee (Co-op Shootem up)
For the fun, you wouldn't pass level 1! (Challenge accepted?)
Super Ghouls and Ghost