Um let's see: Crown Princess, Corpse Princess, Guilty Crown, and Kurokami (not really what you said but it's one of my favorite animes.
Sailor Moon. The princess is a "ninja" and has a bunch of female warriors that protect her as well as one male, the prince, who fights too. the "monster of the day" theme gets kind of sappy at times though. The English version released in America has been sterilized for children. The good stuff will be found in the Japanese version with English subtitles. Its an 80s-90s cartoon so if you don't like nostalgia cartoons from back-in-the-day you might not like it. there were several seasons amounting to 200 episodes or so and I think one or two movies. the Anime version does not completely match the Manga... the Mangas are really beautiful though and in the end the princess of the moon and the prince of earth get married