If what you want is a horror anime that makes you think instead of being bloody, than the best has not been mentioned. Boggie Pop Phantom is an amazing, psychological story.

My favourite character is Poom Poom. He started as a simple character in a childrens' stroy that a highschool girl wrote. After her guidance counselor told her that she could never be a writer she burnt all her manuscripts. When this happened Poom Poom emerged into the real world. His purpose is to make everyone happier, but he found that he couldn't find anyone who was quite sad enough, so he messes with people's minds until they fall into a deep depression. They sometimes kill themselves. Once they are in this depression, everyone needs to be around Poom Poom just to feel the least joy. Poom Poom becomes a living drug.