Seeking a particular brand of villain

[Seiryuu]

I've been wondering whether there are any anime/manga, particularly mysteries, with a certain type of truly terrible villain who frequently taunts the heroes, toys with them and even tortures them, but never actually shows his/her face. This sort of villain often takes great interest in his investigators or specific parties involved in the cases, making it into a sort of battle between them. However, while he will frequently mess with the heroes through messages, specially selected crimes, or even fakes and proxies, he never shows his true face, leaving the heroes with no way of knowing just who they're really fighting.
A perfect example of this from American TV is Red John of The Mentalist. This guy's made certain to hide himself thoroughly, never showing himself for real, but constantly toys with the hero Patrick Jane, sending messages from time to time to taunt him, using people to get to him, selecting victims for impact and challenging him at every turn, even getting rid of anyone who can get in the way of their "relationship". This is made even worse with some hints that the true culprit might be someone he knows.
Another example that's coming to a close is the villain of Danganronpa. This person is even more determined to stay hidden (until identified), playing a godlike master of the prison the characters are in, with the sole express purpose to bring every last one of them to ultimate despair.
I've seen enough mysteries where there's a new villain every one or two episodes, and I've seen a few mysteries as well where the villain deliberately and regularly shows his face, so everyone knows who he is and where he is and knows immediately when certain crimes have happened that he did it and how. Both bore me and often are quite lacking in real suspense and intrigue. Give me villains who are smart enough to stay hidden, sadistic enough to go beyond anyone's expectations, but arrogant and dramatic enough to stick around and play with the people who want to catch them. Bonus if there's an implication that it may actually be one of the hero's own allies or close companions.

[Kotohono]

If a more grey antagonist instead of true villain works, then definitely Code Geass and Death Note fit this.


Additionally I'll suggest Psycho-Pass, the main villain plays this role very well. And Robotics;Notes should fit too.

[kitten320]

Ga-Rei Zero kinda fits.

Magical Madoka kinda fits. Kyubey is messing with everyone lives but no one realizes until it is too late.

Mirai Nikki - all antagonists remain hidden.

[Triple_R]

I second Psycho-Pass. The main antagonist in that show fits your description pretty well, imo.

[SeijiSensei]

Johan makes the occasional physical appearance in Monster, but most of the time he is off-screen pulling strings.

[Sackett]

Soul Eater for most of it anyway.

Maybe Katanagatari and Penguindrum

Tiger & Bunny, Chrono Crusade

[Jan-Poo]

Originally Posted by SeijiSensei

Johan makes the occasional physical appearance in Monster, but most of the time he is off-screen pulling strings.

20th century boys from the same author fits the bill a lot better.

Seiryuu didn't quite specify if this villain must be as much as hidden to the viewers/readers than he is to the protagonists, but if that's the case then Monster doesn't quite work for the most part, since the villain's identity is quite clear.

[Seiryuu]

Hidden is preferred since it adds to the suspense, you don't know who it is and there may be a good chance the enemy is someone close and completely harmless-looking. I still remember speculating after watching a bit of Higurashi about the tension that one could feel knowing that someone in a group is a cold-blooded killer, if everyone in the group was kind and innocent and a good friend, so no-one's really suspicious and there's nothing to make anyone look any more safe than the next person. Also, the ultimate villain of that series turned out to fit the bill quite well now that I think about it, manipulating things to exploit terror and encourage outbreaks of paranoia for the sake of research, while keeping their identity hidden (granted, the person's eyes and personality made me a little cautious).
With minimal stretching, one could also consider the villain of Shion no Ou to be in this category. His identity isn't revealed until very late, and until then he stays in the shadows watching and torturing his chosen opponent while manipulating everyone. Unlike many of these villains, he doesn't actually take any interest in the cops though. Instead, he takes a frighteningly obsessive interest in a little girl barely out of grade school, seeking to push her to the breaking point to make her an ever stronger potential adversary. While he certainly doesn't seem to sadistically enjoy causing pain, he very much has that narcissistic viewpoint, like he's playing a chess game and everyone else is just a piece to be moved as he sees fit.

[SeijiSensei]

He also provides one of the stupidest reasons for committing murder I've ever heard.

(Warning: Link is a spoiler.)

[Seiryuu]

Originally Posted by SeijiSensei

He also provides one of the stupidest reasons for committing murder I've ever heard.

(Warning: Link is a spoiler.)

Big difference between stupidity and insanity. I didn't say he was sane, just that he was arrogant, brilliant, and kept his identity hidden throughout the story while still repeatedly taking steps to torment Shion and mess with her mind for his own ends. Intelligence-wise, he's brilliant, just twisted. Also, I've heard that a lot of great masters believe they can tell a good bit about a person's talent from as little as one game, and if she was demonstrating some real insight and strength so soon after learning how the pieces move, then she definitely qualified as someone with great potential, enough so to catch his attention. True, he was insane to think he could make a four-year-old grow the way he wanted so easily, or that trauma and isolation would inevitably foster strength in anyone, even a little girl. But he still managed to completely conceal his identity and even manipulate things behind the scene to bring about his ends, and to thoroughly torment his chosen opponent over a long period without revealing his face.
Anyway, I only said he's a relatively good fit, different people's views of the story could change how well he fits to you.

[Kotohono]

Originally Posted by Seiryuu

Hidden is preferred since it adds to the suspense, you don't know who it is and there may be a good chance the enemy is someone close and completely harmless-looking.

Robotics;Notes definitely does this, though pace might not be what you're looking for.

And Penguindrum might actually fit too.