@zfreeman stole most of my thunder. Let's see... Also great:
Asterix
X-men
Sunset riders
... And a few lesser known :
Vendetta : a beat em up that somewhat has the same style as final fight but has more weapons (including bricks and a shotgun).
Penguin bros: a platformer in the style of bubble bobble and snow bros(also good games, BTW). You play as a penguin that can lay bombs. The idea is to eliminate enemies by using the canons and seesaw to hurl these bombs at them
Pang: shoot the bubbles above you into smaller ones. Plenty of levels (on many platforms, even), but there's something very elegant about the original arcade game
Logic pro: you know griddlers/picross puzzles? This obscure Japanese game is that... On crack. It's weird and stupid, but damn is it addicting if you're into puzzle games