White Town: Your Woman
When the theme was announced I thought of this song and this song alone. Admittedly, other than covers, I can't think of one song that was more memorably a gender bender than White Town's one-hit-wonder "Your Woman" from 1997.
The incredible catchy electro-pop hit managed to rise up the charts despite (or maybe because of) it's strange gender-bending qualities. White Town was the musical project of Jyoti Prakash Mishra, and the song was a re-working of a classic Bing Crosby song that was originally "My Woman". So the decision to take it in the gender-bending direction was Mishra's own. On wikipedia he's quoted as saying this about the decision:
When I wrote it, I was trying to write a pop song that had more than one perspective. Although it’s written in the first person the character behind that viewpoint isn’t necessarily what the casual listener would expect.That's for certain! When it came out I suspected it to be sung by a drag queen.