3. Elfen Lied
Hot chic with telekinetic powers, cool! Not really, especially if the girl has been tortured, abused and discriminated against leaving her highly unstable, full of hate and out for revenge. Elfen Lied tells the story of Lucy, a Dicloni girl or evolved human who suffered social alienation due to her unusual telekinetic powers. Depressed and angry, Lucy goes on a rampage and starts killing all who brought her misery. How does she do it? By decapitation and literally ripping people to shreds of course, which makes this violent and dark anime a true legend in the horror anime genre.
Official site here.