It's pretty fun reading through this topic and remembering some old games I've played. For instance, I really enjoyed The Lost Vikings.
My very first platformer was Super Mario Land. That Game Boy game used to make me sweat as I advanced through stages that became increasingly unfamiliar. It's one of those things that can only be experienced when there is no save system, and the only progression is through your increased knowledge of the game. (Another hellish game on the Game Boy is Cosmo Tank: the soundtrack is awesome, but it was brutal!)