Elfen Lied

Elfen Lied (2004 anime, 13 episodes) is a dark, violent, and emotionally intense series blending horror, psychological drama, gore, and tragedy.

Quick synopsis: The story centers on the Diclonius — a mutant subspecies of humans born with small horns and invisible, telekinetic "vectors" (arms) capable of slicing through almost anything at a distance. These beings are feared as a potential threat to humanity's dominance, leading governments and scientists to capture and experiment on them.

The main character is Lucy, a powerful teenage Diclonius held captive in a secret research facility. After a brutal escape (one of anime's most infamous opening sequences), she suffers a head injury that splits her personality: her original violent, vengeful self (Lucy) alternates with an innocent, childlike, amnesiac persona who can only say "Nyu" (hence called Nyu).

Two college students — kind-hearted Kouta and his cousin Yuka — find the naked, injured Nyu washed up on a beach and take her in, unaware of her true nature and deadly past. As they form a strange household dynamic, the government relentlessly hunts Lucy, other dangerous Diclonius appear, and buried traumas from Lucy's childhood (and Kouta's own past) resurface, driving themes of discrimination, revenge, love, betrayal, and what it means to be human.

It's extremely graphic (lots of blood, dismemberment, nudity, and mature themes), often described as a mix of beautiful art/music with unrelenting brutality and sadness. The anime adapts roughly the first half of the manga and has its own ending.