It would be a travesty not to kick things off here with perhaps the most celebrated androgyne in recent anime history, Haruhi Fujioka of Ouran High School Host Club (2006). Anime fans are likely to be familiar with the premise of this popular series, but have a summary just in case:
A frumpily-dressed new student named Haruhi stumbles into a clubroom full of handsome upperclassmen, and breaks an expensive vase. Unable to pay for the damage, Haruhi is forced to earn money by joining their club, which is essentially a PG-rated escort service. He must spruce up his appearance and entertain the school's female population on dates until he has cleared his heavy debt.
SPOILER: The twist is, he isn't a "he."
Males and females alike proceed to fall in love with her. I mean, can you blame them?
As per the jargon of the gender-bending genre, a "trap" usually refers to a male character who appears so feminine as to trick others into believing that he is female. Haruhi, then, might be considered a "reverse trap": a female superficially mistaken for a male.
Yet Haruhi stands out for being, not only superficially androgynous, but also androgynous of mind.