I am looking for a very specific style of anime.

I want it to be a psychological thriller. That sort of entertainment genre that makes you go "Oh... my... god. What was the director on when he did this?" after watching it.

Something on par with Japanese horror films, or like games like Fatal Frame and Silent Hill.

I know there HAS to be animes like this. Any suggestions?

I have thought so with many many titles... but the one that sticks out in my mind is Dark Myth... It is a many series and has a slight pornagraphic side to it. But it is by no means hentai... Another one is Paranoia Agent... or Shadow games but is is Korean not japanese..... all this information has come at a slight price... you must now drop to your knees and worship my ultimate penis.

Perfect Blue sounds like the best fit, although that's a movie rather than a series.

If you're into the real 'WTF' sort of thing then Seriel Experiments Lain, Evangelion, Rahxephon and FLCL might appeal as well. Although I wouldn’t class any of these last few as ‘thrillers’.

Boogiepop Phantom and Yugo the Negotiator are both good psychological thrillers that I would definitely recommend.