When Birdo was introduced to North American gamers in the pages of the Super Mario Bros. 2 instruction manual, there was no question as to the character's gender.
"He thinks he is a girl and he spits eggs from his mouth," the description reads. "He'd rather be called 'birdetta.'"
Subsequent printings of the manual expunged that last sentence--and effectively set the tone for how the folks at Nintendo of American would treat Birdo in the future. (Typically, no gender is assigned to the character--though in the U.S. version of Super Smash Bros. Brawl he is said to be "a pink creature of indeterminate gender.")
The brass at Nintendo of Japan have had no such hang-ups. From the start, the character, called Catherine in that territory, has always been a "he who wants to be a she"--as evidenced in the following Super Mario USA commercial:
Also worth watching if you're part of the is-it-a-he-or-a-she set: The "Birdo is Male Proof Video."
One portion in particular blew my mind when I watched it for the first time earlier today--that being the portion that suggests (based on the Japanese website created for Mario Kart Double Dash!!) Birdo/Catherine is Yoshi's boyfriend.
So, not only is Birdo transgender in some way, but Yoshi is gay to boot!