One of the biggest mysteries brought forth in the third generation was Mirage Island. This seldom-seen island is tipped off in game by an old man in Pacifidlog who tries to view it each day. It rests on Route 130 but is only ever accessible under most curious circumstances.
Every day at midnight a random number going up to 65535 is generated. If this number matches what the personality value of your Pokemon is when divided by 65536, you will be granted access to the island for a day. This number is fixed during the day and thus even if you deposit the winning Pokemon in the PC you can still go onto the island. For some reason if your in game clock maxes out the numbers are no longer generated, so you better hope that happens on a day you can go to the island!