I was playing a game with a rogue who's backstory was essentially "I want to build a bunker to be safe." Erm, ewkay. Apparantly his character was also a coward. The party would be exploring caves and he would be "guarding the cart" (never ran off with it, thankfully) and almost got himself whacked when he pulled his sword on some hoochies the witch sent to him as a joke. He was like a really cowardly Batman, always brooding about something.
Now here's another one from a friend who was in my game and played a halfling inquisitor. He wanted to make the most ridiculous backstory as a joke. So he made up a cult called the Truth of the Beard or something which had different orders depending on how the beards were cut. Longbeards ran everything and his character was part of the assassin order called the Goatees and he got in trouble for sleeping with the Longbeard High Priestess who was the Great Longbeard's daughter. So he was on the run from the Great Longbeard and the Goatees. I allowed it.