Another game I can almost say I 100%'d, but can't because it's a luck-based challenge, is Earthbound. One of your party members has exactly one weapon in the entire game, the Sword of Kings, and it's an extremely rare 1/128 drop from a fairly difficult enemy that's in exactly one point of the game. Once you complete the dungeon he's in, he stops spawning altogether.
I ground Ness up to level 99 trying to get that stupid thing and never got one. And that's before you get the massive experience & stat boost from completing Magicant.