Mine may have been Super Mario Bros 3 as well. It could have been that, Super Mario World, Donkey Kong Country, Super Mario World 2: Yoshi's Island, or Ocarina of Time. Link's Awakening I remember playing very young, but I didn't finish it until after I had finished Ocarina of Time. I was stuck on the second dungeon for many years not knowing that you needed magic to light a torch. I know for a fact that I beat Ocarina of Time in early 1999 after getting it for Christmas of 1998, but I don't know if I finished any of the other games mentioned first. I definitely played Super Mario Bros 3, Super Mario World, Donkey Kong Country, and Super Mario World 2: Yoshi's Island for multiple years before playing Ocarina of Time, but I could easily imagine myself getting stuck in various points in those games. For example I remember the snow level in Donkey Kong Country being a huge problem for me for a long time. Pokemon Yellow is another possibility - I think I got that shortly after release in 1998 and being able to grind experience makes it easier to beat than purely skill-based games.
The other games I played a lot but didn't finish for 15+ years were Goldeneye 007 and Donkey Kong Country 2. I did beat Goldeneye 007 on Agent and through Cradle on Secret Agent as a kid (I have a photo of myself playing Aztec in 1998 or 1999 - need to double check), but I don't count that as it's not the whole game.
