Ninja Gaiden: It is actually a "go slow and carefully" game, not a "run through frantically" one. Once you realize this and watch for enemy spawn patterns, the game becomes way easier. As long as you go slow, the game rarely has you fight more then 1-2 monsters at a time. Sure, they still put some spawn points at the edge of ledges to really mess you up, but you can usually watch for the pattern and figure out how to get through it pretty easily. Plus, even with this method, the time limit is rarely an issue.
Edit: Another one for NES/SNES games in general: Very few have true "randomness", everything is usually done by a pattern. Think of them like puzzle games rather then action games, you just need to put the right button combinations in at the right time.
I feel like I need to put something here, or else I am one of those weird people who think that having no signature is a character trait.