-If you manage to beat all of A Link to the Past without getting hit once, you'll be rewarded with a second quest where you can use the legendary Black Sword.
-If you use gameshark to walk through walls in Pokémon, you can skip fighting your Rival after the Elite Four and Oak won't show up in the Hall of Fame, you'll then be free to explore the Hall of Fame. If you walk all the way to the right, you'll come across a room with a hospital bed, laying in the bed is the legendary Pokémon "Pikablu". (this one I still have vivid memories of from my imagination, i can picture what the room "looked like" back when I used to think about it as a kid).
-There were about a billion and one rumors about getting Luigi in Super Mario 64.
-The Ice Key in Banjo-Kazooie. If you managed to fly directly into the Walrus Cave (or whatever it was called), and do a bird dive into the barrier blocking you from the Ice Key, then it will break and you can collect the key.