Not a genre but actually a demographic. Refers to anime based on manga that was originally serialized in a magazine targeting girls of any age. American fans seem to often be confused and classify any show that has romance and/or major female main characters as shoujo-- this is wrong.
Anime based on manga targeting young women would be called josei. (though very little of the manga targetting young women gets made into anime-- the only ones I can think of are Ebichu and Momoiro Sisters.)
Titles that deal in might and magic will fall into this category. Inuyasha and Tenkuu no Escaflowne are a couple of titles which fall into this genre.
