Not seriously off-the-wall, but when our DM came up with a campaign concept where we started out as having just killed the dragon who's been terrorising the kingdom, and the adventure was to make it safely back to town in order to claim our reward, I built an Oath of Vengeance paladin whose oath was... to kill the dragon.
So he starts out like Inigo Montoya at the end of The Princess Bride - he's spent his whole life in the vengeance business, and has absolutely no idea what to do next.
He was very un-paladin-like in style and attitude, a tough-as-nails mercenary with a massive two-handed maul and a cynical dislike of organised religion.