Moral Sociopathy

Sociopaths are essencially the human version of Exclusively Evil in media. Since we consider morality to be good, they are naturally depicted as amoral and selfish.

While it is somewhat Truth in Television, sociopaths are still human, and it's not unnatural that sociopaths have a sense of right and wrong, even though it is completely different from what other people consider that to be. Many diagnosed sociopaths are known to have moral codes, either unique to them or already established. Naturally, since these types of morality focus more on abstract concepts rather than the people themselves, expect some rather nasty extremism.

See also Principles Zealot, when a villain is completly obsessed with his/her moral code; many moral sociopaths are these as well, as they care more about their moral code than people themselves. However, moral sociopaths need not to be always overwhelmed by extremism; some can be more Noble Demon types, which while lacking empathy, still have a moral code to restrict them in some ways. Also compare/contrast Black and White Insanity and Sociopathic Hero.

This is not to be confused with Ubermensch. Moral sociopaths can have their own unique moral codes, but they are just as likely to adhere to already established things like Christianity and Communism.

No Real Life Examples, Please.

Anime and Manga

 * Zolf Kimblee from Fullmetal Alchemist is perhaps the most iconic example in anime. While he is an Ax Crazy Mad Bomber, it is well established that he does have a sense of honour, although a rather twisted one.
 * Vino from Baccano! is the sort of person best summed up as "Ax Crazy Awesome." For someone who likes to grind people's faces off on train tracks, he gets very annoyed when someone attacks an uninvolved bystander.
 * Fleet Admiral Sakazuki from One Piece, His code is of absolute justice untempered by mercy or restraint.
 * Black Butler:  wants a world of purity and light. Burning cities, murdering children, screwing dogs, whatever it takes.

Comicbooks

 * Doctor Doom
 * in Fables, combining the worse of an Evil Overlord and a Knight Templar, much to the dismay of everyone else.

Film

 * The Hunchback of Notre Dame: Frollo is selfish in his lust for Esmeralda, but otherwise he sincerely believes half of the things he does genuinely are what God intended (albeit because he, Frollo, couldn't possibly do anything God didn't want him to do). A pretty big break from the literary version, who was a much nicer Anti-Villain and probably not a sociopath at all.
 * Mr. Blonde from Reservoir Dogs cuts a man's ear off for fun, has no sense of professionalism, indiscriminately guns down innocent bystanders, and clearly has no regard for his fellow robbers or their well-being. On the flip side, he appears to have a great deal of personal loyalty to his employer Joe and is shown (in a flashback) to have refused a plea bargain and instead serving a jail sentence when he could have walked by implicating Joe in a smuggling operation he was caught in.
 * According to the creator's commentary, in Kung Fu Panda 2, Lord Shen exhibits traits of this. He knows how utterly horrendous his actions were, but he refuses to admit how wrong he was about his parents because it's the only way he can justify the genocide of the pandas. As far as he is concerned, it's too late for his redemption and rendering everything as accidents is unthinkable.

Literature

 * In the Night Watch series, the worse members of the Light Ones are this.
 * Subverted with Hrathen in Elantris, who seems like a religious fanatic at first, but turns out to be one of the more reasonable antagonists and goes through crippling guilt for his actions- he supports his theocratic religion because he believes it is too logical and well-organized to be wrong ..

Live Action TV

 * If we are to take him at his word, Sherlock Holmes is a more-or-less-heroic example of this trope in Sherlock. He solves difficult crimes for the intellectual challenge rather than any particular desire to right wrongs or help people.

Tabletop Games

 * The phyrexians from Magic: The Gathering qualify big time; they have a very well structured religious system and many of them hang neurotically to their philosophy, but they have so little empathy that Complete Monster might as well be their hat. New Phyrexia indeed has two factions that fit this bill perfectly: the Machine Orthodoxy, composed of white aligned phyrexians that formed a nightmarish faith which they cling to obsessively, and the Progress Engine, composed of blue aligned phyrexians whose view of "progress" would make Josef Mengele proud.
 * The Azorius from Ravnica also count, being obsessed with order and making laws, while not caring for the population, and sometimes even acting fascistic. White and Blue really love this trope.

Video Games

 * Jade Curtiss in Tales of the Abyss is a heroic version. He has no empathy whatsoever, but is troubled by this, and always tries to do the right thing even though his concept of right and wrong can be a little skewed.
 * Sofia Lamb is a curious case in that she probably did not began as this, being originally driven by her altruistic goals (though arguably she was enamoured with the concept rather than the people themselves), but by the time of the game she became a Totalitarian Utilitarian obsessed with removing individuality and curing humanity's genetic fatalism.

Webcomics

 * Kore from Goblins. He does sincerely believe he is doing the right thing by mercilessly slaughtering everyone that has been in contact with "evil races", even children of his own species that were with said "evil races".