Elfen Lied

The Diclonius, a mutated homosapien that is said to be selected by God and will eventually become the destruction of mankind, possess two horns on their heads and have a "sixth sense" which gives them telekinetic abilities. Due to this dangerous power, they have been captured and isolated in laboratories by the government. Lucy, a young and psychotic Diclonius, manages to break free of her confines and brutally murders most of the guards in the laboratory where she is being held, only to be shot in the head as she makes her escape. She survives, falling off a cliff into the ocean and manages to drift along to a beach where two teenagers, Kouta and Yuka, discover her. Having lost her memories, she was named after the only thing that she can now say, "Nyuu," and the two allow her to stay at Kouta's home. However, it appears that the psychotic side of Lucy is not dead just yet... (Source: ANN - Revised)

Mahoromatic: Automatic Maiden

Vesper is a secret agency fighting an army of alien invaders by using super-powerful battle androids. Mahoro is Vesper's most powerful battle android and has won many battles, but she has little operating time left and soon will cease to function. However, if she lays down her arms and conserves her remaining power, the time she has left can be prolonged to just over a year. Mahoro is given an opportunity to live the remaining time she has as a normal human. She chooses to live as a maid for Suguru, a phenomenally messy high school student who lives by himself after his family passed away. (Source: Anime News Network)

Fractale

The story takes place on an island, where a "Fractale System" is beginning to collapse. One day, Clain finds an injured girl called Phryne under a cliff. She disappears leaving a pendant. Clain sets out for a journey with the girl-shaped avatar Nessa to look for Phryne and discovers the secret of the Fractale System.