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)

Another

When Kouichi Sakakibara transfers to a new school, he senses a frightening atmosphere in his new class, a secret none of them will talk about. At the center is the beautiful Mei Misaki. Kouichi is immediately drawn to her mysterious aura, but he begins to realize that no one else in the class is aware of her presence. Soon after his arrival, what is known as the Calamity begins, and it claims the lives of many students. (Source: Sentai Filmworks)

Vivy -Fluorite Eye's Song-

An AI named Matsumoto appears before Vivy, the world’s first autonomous humanoid AI. Matsumoto’s mission is to rewrite history together with Vivy, in order to stop the war between AI and humans that will happen one century later. (Source: Funimation)

Code Geass: Lelouch of the Rebellion

On August 10th of the year 2010 the Holy Empire of Britannia began a campaign of conquest, its sights set on Japan. Operations were completed in one month thanks to Britannia's deployment of new mobile humanoid armor vehicles dubbed Knightmare Frames. Japan's rights and identity were stripped away, the once proud nation now referred to as Area 11. Its citizens, Elevens, are forced to scratch out a living while the Britannian aristocracy lives comfortably within their settlements. Pockets of resistance appear throughout Area 11, working towards independence for Japan. Lelouch, an exiled Imperial Prince of Britannia posing as a student, finds himself in the heart of the ongoing conflict for the island nation. Through a chance meeting with a mysterious girl named C.C., Lelouch gains his Geass, the power of the king. Now endowed with absolute dominance over any person, Lelouch may finally realize his goal of bringing down Britannia from within! (Source: Bandai Entertainment)

ERASED

Satoru Fujinuma is a 29 year old manga artist struggling to make a name for himself following his debut. But, that was not the only thing in his life that Satoru was feeling frustrated about… He has a unique supernatural ability of being forced to prevent deaths and catastrophes by being sent back in time before the incident occurred, repeating time until the accident is prevented. One day, he gets involved in an accident that has him framed as a murderer. Desperate to save the victim, he sends himself back in time only to find himself as a grade-schooler one month before fellow classmate Kayo Hinazuki went missing. Satoru now embarks on a new quest: to save Kayo and solve the mystery behind her disappearance.