In a serious military fantasy campaign, there was a guy who proposed a character build using a homebrew cross-dresser character class. He was denied.
In my first Freeport game, I had a character who played an awakened gorilla named Queequeg.
I once had two characters who had a shared backstory; one was a hobgoblin who was nearly killed by the other character in a raid when she discovered that she was a barbarian. The barbarian didn't recognize the hobgoblin, and he was careful to hide his massive scar from her until they finally gave that away... while in flagrante delicto.
I had a character who was a seriously psychotic Don Juan womanizer. He ended up getting turned into Fast Times era Phoebe Cates for a while. Granted, the player didn't ask for that to happen, so I guess it wasn't so much an outrageous request, as just something outrageous that happened to him.
I had a player buy a slave for anthropomancy once. The rest of the group weren't really quite down with that, so he did it at night while they were sleeping.