Two games:
Captain Comic. Horrible platformer. But winnable, even as a kid. Plus it plays whistling Dixie or Yankee doodle or something when stuff happens. Nothing happens. I never knew how quickly winnable or broken the game was when I was a kid. Then I watched speed runs.
I still like it.
Transbot (for the SMS). A shoot 'em up that just looped 2 very distinct levels continuously. I've always wondered if it is actually possible to finish it, maybe after 50 or 100 level switches or something. I never got there. It might have been after 10 and I'm just shit at it. It did have various weapon types (but you mostly used the big C one for normal stuff, or the rocket D one to go to the other level), it did have cheat codes (slow weapon cycle and more lives?), it had a boss that fired more and more between level switches (pray to god that you manage to switch levels later in the game, or hunter yellow thingies and the nuts and bolts and barriers will get you) and it had plenty of challenging enemy types. I tend to think that people severely underestimated it. It got hard as hell. It came with my Sega, and I still load it up once or twice a year through an emulator to this day. It is great for a half drunken high-score challenge against a mate. I seriously want to make a part 2 of Transbot at some point. It was awful, but great in so many ways. Even the box-art was exactly representative of what level of gameplay you should expect from it (I don't think you got a box if it came along as the packaged game with the Master System. The card fortunately had an exact copy of the box art on it). Superb!