[KuroiBara]

List of Anime/Manga I know of and watch often (you may want to Google these for descriptions)

-Death Note (Shinigami, slight love story, slight violence, supernatural in ways, good story line)
-Rosario + Vampire (can't remember if there IS an anime for this, but there is a manga. It's quite Ecchi [can't spell that word, sorry!] but there's a love story with violence. Only human in a school full of monsters, falls in love with a vampire)
-BlackBird (again, not sure if there is an anime, but it's love/violence. The whole supernatural thing again with demons and humans in love)
-Pandora Hearts (quite elegant I guess, good story line, guy falls into an abyss and comes out same age as he went in etc)
-The Girl Who Leapt Through Time (love story, time travel)
-Tales From Earthsea (I've forgotten the story to this, I haven't seen it in ages)
-Princess Mononoke (again, not sure of the story, It's been quite some time)
-Chobits (admittedly I am unsure if there is an anime as I have never got past chapter one of the first book. I hate libraries that close early!)
-Spirited Away (not sure how to describe it... Cute, funny, good story line)

Those are all I can think of... I've seen/read a lot more, I just can't think right now.
I hope some of these are helpful. Without a good idea of the type of person your girlfriend is and the things she likes, I wouldn't be able to give accurate suggestions, but those are some popular manga/anime amongst a lot of the girls I know.