I don't really watch horror anime, but I do like some anime with darker themes, I guess. But really, if you're trying to get acquainted with the anime world, these are MUST sees:
Death Note
Premise: Shinigami, or gods of death, all possess Death Notes, which are supernatural notebooks. If you write a human's name in the notebook, that person will die of a heart attack in 40 seconds. The shinigami who writes the humans name in the Death Note then receives that person's remaining life span. Well, one day, genius, idealistic Light Yagami (a human) finds a Death Note on the ground outside of his school and after testing it out and realizing it isn't a hoax, begins using it to try to rid the world of criminals and evil. After the police notice all these criminals dying of heart attacks by mass murder "Kira," they suspect somebody of orchestrating this and begin trying to solve this mystery with absolutely no physical evidence. In order to do so, they bring in the world's greatest detective, L. Because no one knows his name and no one sees his face (he talks to people through a computer), Light can't kill him using the Death Note. At the same time, L has no idea who the identity behind mass murderer Kira is. Anyway, it's really good, and it's dark, and kinda creepy. It's a psychological thriller, and I think that basically every anime fan has to have watched Death Note
Fullmetal Alchemist: Brotherhood (watch Brotherhood because it follows the manga and the manga's better than the 2003 anime)
This anime follows the story of two boys who are alchemist prodigies - Edward and Alphonse Elric. When their mother died when they were probably around 8, Ed and Al attempted to use human transmutation (a taboo in alchemy) to bring her back to life. When the alchemical ritual goes wrong, Edward loses his right arm and left leg and Alphonse loses his entire body, only surviving because Edward used alchemy to bind his brother's soul to a suit of armor. Because of that, Ed and Al began chasing this legend, the philosopher's stone, which is said to magnify an alchemist's power, in order to attempt to get their bodies back. And, due to their pursuit of the philosopher's stone, they begin to discover truths about their country and the military that they could have never imagined. This anime is probably my favorite, EVER. It has amazing characters, a phenomenal plot, and a good amount of action/fighting. Plus, there are several homonculi, which are artificially created humans, who can't die. IDK if that fills your request for monsters.
So, I think you should DEFINITELY watch these two! Other anime you might enjoy (they're all darker, not necessarily horror, but are dark)
Code Geass
Blood+
Attack on Titan
Bleach
xxxHolic is a little creepy I guess...
Edited by Win-chan, 13 July 2014 - 10:48 PM.