Donkey Kong, originally for the Gameboy, is a fantastic game. It starts with classic arcade-style levels but quickly expands both Mario's moves and the complexity of the environment. The final battle with DK was one of my best memories playing the old Gameboy as a kid.
Castlevania, Ninja Gaiden and Zelda are my personal favorites. They do have problems: Castlevania requires some pretty precise platforming that can get frustrating, Ninja Gaiden gets exponentially hard with the last two levels and Zelda is really cryptic.