In Zelda: Ocarina of Time, you could unfreeze the Zora lake.
Or, that after you beat the game, you could find another Ganon with blue hair, and once you beat him, there's new stuff in the game.
Or that you can bring the first town back to normal when you're adult.
In FF7, you can revive Aeris, and Sephiroth can join your team.
Or that you can have more color of Chocobos. (how do you spell that?

)
In FF Tactics, once you beat the game, sometimes you could continue to play, and you have new jobs and stuff.
And you know what?
I used to believe all of them when I was a kid.