It was definitely something on the NES. Could have been Super Mario Bros, Double Dragon, Teenage Mutant Ninja Turtles, Megaman 2 (I'll always remember that the second Megaman was the first of the series that I played), Bugs Bunny's Birthday Blowjob... Had to be one of those and could have been any one of them.
If I absolutely had to guess, I'd say it was probably either Super Mario Brothers or Double Dragon. Goodness, the original Double Dragon used to haunt me so much as a child because I loved to play the game so much but it was just so hard to beat (thankfully, I have long conquered it since then.)