Birdo
Birdo is a strange creature that first appeared in Doki Doki Panic (AKA Super Mario Bros. 2). According to the instruction manual, he is a boy that likes to be called Birdetta. However, in the credits, Birdo is shown as Ostro, which is another type of enemy and is nothing to do with Birdo.
In later games, Birdo has been female (rather than a male who wishes to be female), and also seems to have become Yoshi's girlfriend in some games, proving that Birdo is definitely female.
In Mario & Luigi: Superstar Saga, Birdo eventually replaced Bowser as Popple's "rookie". She seems to have fallen in love with Popple.
Most people are beginning to think that Birdo is a transvestite, but others have cleaner minds and just think that he/she is a very, very, very strange creature. Besides, you know, there could just be more than one of them, each varying in gender.
In Japan, she is more widely known as Catherine, which was accidentally leftover in the Wario's Woods English manual.
