A prominent figure was Elfen Lied, a 13-part anime television series based on the one written by Lynn Okamoto and drawn manga Elfen Lied builds up, recommended. And I have to say, I really like the bloody carnage at the start of the series.
The core of the story are the "Diclonius", they seem to be the next stage of evolution. They are creatures with horn-like deformations on their heads. They possess powerful telekinetic powers, which manifest themselves in the form of invisible arms. With these powers, they could easily wipe out humanity. Fearing this, some Diclonius are imprisoned from birth (they cannot use their powers immediately) for better study. Others are killed instantly. One day one of the Diclonius (Lucy) manages to escape. On her escape she cuts a bloody path through the ranks of the guards. However, she ends up with a bad head injury, falls into the sea and when she regains consciousness she has lost her memory and is as innocent as a child again. Lucy is picked up by Kouta and Yuka on a beach. From now on, Kouta and Yuka will call her "Nyuu" because she can't say anything but Nyuu. From this moment on, these three live together in one house, unaware of the impending dangers that are yet to lurk.
Below is the complete series in 13 parts, starting with Episode 1 “Encounter”: