Best Psychological (Or Psychological Horror) Anime You've Seen

Psychological... huh. FMA is really good, I think(Fullmetal Alchemist). Parasyte is a more horror-oriented one, though it has some deep thoughts too. OH WAIT --> Assassination Classroom is really good, not as much horror as kind of humor, but deep thought as well(read the manga if you can, anime only goes so far)

 

NHK ni Youkoso is by far the best psychological anime I've seen. A guy gets so paranoid about conspiracies and other people around him locks himself in a room for nearly 4 years, then he meets a girl trying to help go outside and fit in with society. It's not necessarily a horror anime, but it definitely does get quite dark at times. There's a ton of laughs to be had too. If there's one 'serious' anime I'd recommend, it'd be this one. Especially because of the realism and the thought that this could happen to anyone and could be happening right now.
A clip from the anime itself to give you an idea.
But yeah, I cannot stress enough how good this anime this >_>

 

Puella Magi -freaking- Madoka Magica. Especially Rebellion.

 

To be honest, Psycho-Pass is the only anime that came to mind right away, I'm surprised nobody has really brought it up yet. The whole anime and its sequel, Psycho-Pass II, revolve around an authoritarian future dystopia where all of the citizen's have a "psycho-pass", which is a measurement of their psychological state, and if it's too high the person will either be subject to lesser penalization or outright termination depending on how high it may be. In other words, if the person may be considered too dangerous to the society, they are to be annihilated due to the system that governs everything suggesting that there's no hope for them. I could get into much more detail than that, but if you may like action and crime related stuff, Psycho-Pass is for sure something to at least check out.