Like the title of the thread says, I'd like to hear about any of your favorite Anime series/movies that focus on the creepy factor. Things like "Perfect Blue", "Boogiepop" and "Lain". Stuff that makes you think. Gore and/or nudity doesn't bother me, but neither should it be the main attraction. I want stuff that makes you think and draws you in. Any thoughts?

You should try either Higurashi No Naku Koro Ni or Neon Genesis Evangelion. Both are really good. I'd say go for Higurashi if you like suspenseful/psychological horror/ mystery thrillers (that surprisingly has very little gore in the first season) that really fucks with your mind. Evangelion if you like deep, complex characters and slowly going into depth of their psychological torment (and insanity). But if you like emotionally/mentally unstable characters, I'd recommend you watch both.

I've seen bits of Evangelion before, that seemed pretty good. I'm just so far behind in my anime watching I never got around to watching the whole thing.

Well, I've got it covered for Scary/psychological/creepy stuff, just not anime. :/

I don't know about anime, but I loved reading
MPD Psycho, NOiSE manga

Madoka Magica is my recommendation.

The idea that becoming a magical girl can be a slow death sentence.

Umineko No Naku Koro Ni is a good alternative to Higurashi.

Otherwise, I might recommend "Doubt" and "Judge" by Tonogai Yoshiki. The latter is barely ever updated though