Elfen Lied

It's about a non-human girl called Lucy, who has escaped from an intitution and lost her memory as a part of her split personality. When acting as Lucy, she is a cold-blooded killer, a "diclonious", who remorselessly kills those who hurt her or get in her way.

A diclonious is a being who, although looks human in appearance has extra arms [known as vectors] which are invisible, and a set of horns resembling cat ears. These beings are considered to be violent killing machines  - their soul purpose being to destroy man-kind.

When she becomes Nyuu, she is as innocent as a child and just as sweet. She, Yuka, Mayu and Nana all end up living with Kouta, who, as a child, lost his entire family... Yuka, his cousin, is in love with him and together they manage the family that has pulled together. Nana is another diclonious, though she does not have the same will to kill and violent personality as Lucy. She is set free from the institution agaisnt orders after a violent encounter with Lucy leaves her in a near death state. With nowhere else to go, Mayu brings her to live with their makeshift family. Mayu is a young girl who ran away from home after being sexually abused by her step father. After living on the streets, Kouta and Yuka adopt her. As the anime progresses, we watch as the dicloniuses fight for their right to live, love and stay hidden.