Based on a game by Alice Soft.

What are some great psychological anime?

Considering the fact that you've alrady named a lot of good psychological anime I would like to to go through a few not mentioned . 1)Boku Dake ga inai Machi AKA Erased:(Still airing) Genre: Mystery, Psychological, Supernatural anime. It has a really interesting story line and is mainly an anime that revolves around a mystery.Its been less than 3 months since released but it already shot up to the 5th position according to MyAnimeList and that's a well deserved rank.The animation is also good. 2)Dan Detective School Q AKA Tantei Gakuen Q: Genres: Comedy, Drama, Mystery, Shounen. Just as the name suggests this is a detective anime that revolves around 5 aspiring detective teens studying in the best detective school.Its more of a mystery anime than a psychological one but I can guarantee you will like it.The cases are mind blowing and most possibly the best ive seen so far.The anime was aired in 2003 so the animation is pretty old but its not bad. 3) Zetsuen no Tempest: Genres: Psychological, Action, Drama, Mystery, Magic, Fantasy, Shounen. 2 extremely clever main characters who get mixed into the fantasy world. Though the story gets complicated the thought process of the main characters will never fail to amaze you. 4)Zankyou No Terror: Genres: Psychological ,Thriller Once again 2 extremely intelligent main characters who seem to have a complicated personality in the beginning.
The ending is something one wouldn't usually expect.
This anime cannot be expressed in words.
You must watch it to understand its elements. 5)Welcome to the NHK: Genres: Comedy, Drama, Psychological, Romance This is one really perfect explanation for a psychological anime.
Not to forget the fact that the protagonist himself has lot of psychological issues and the anime is about how people look at him and how some try to help him.
The anime is undoubtedly the perfect for this genre(maybe competed only by psycho pass and death note) but it also has a few drama elements that actually make some people like it more while others feel its a bother. 6)Tokyo Ghoul: Genre: Action, Horror, Supernatural, Psychological, Mystery, Seinen, Drama This is one anime that is a MUST WATCH.
But the only reason why its at the bottom of the list because of the uncertainity of the genres.
Its true that the anime has heavy psychological elements to it and the very existence of the protagonist and his life is a psychological confusion.
The psychological elements of this anime are similar to Parasyte's.
It makes you question your idea of righteousness and wrong.The action and animation are over the top and so is the gore.