Darker Than Black: The Contractors are this in theory (and popular belief in-universe), but Hei at least is proof this isn't necessarily the case. Then again, Hei isn't a true Contractor, and he's arguably more sociopathic than most, since his most pronounced character difference seems to be that he can become angry.
Akagi has some sociopathic qualities. He has no regard for his own life, can't be threatened, doesn't care about rules, will cheat if he can and generally doesn't really care about other human beings. He isn't really malevolent, however, unless you manage to piss him off.
Light Yagami, the Villain Protagonist of Death Note, becomes one as the series progresses and his ego expands. By the time his father dies, Light is more upset that his father failed to do what Light wanted of him than the fact that he's dead!
Light was probably a successful psychopath all along, the kind who make up a large percentage of world leadership rather than the kind that make up a large percentage of the prison population; he degraded into the more antisocial kind with the possession of the nasty book of death. He's slightly more empathetic in his relatively nice and highly-socialized period where he'd lost his memories.
Mello's also a strong candidate, given his aggression, tendency to put himself and others in danger, and superficial charm. On the other hand, the author has pointed out that he doesn't think Mello was an inherently bad person, because he shows genuine empathy for his accomplice Matt, and there are moments where it seems like he doesn't actually hate Near as much as he thinks he does. While he has strong aggressive personality disorders, he probably isn't a full sociopath.
Misa Amane, too. The histrionic kind. In one of her earliest appearances she's quite calmly contemplating how to kill Rem just because it would probably be more convenient. The fact that she fiercely and insanely pair-bonds to Light doesn't actually make her less of a psychopath, it just makes her one with poor self-esteem.
Sakyou from YuYu Hakusho is a textbook example. As a child, he lived a normal life and had loving parents and siblings, but later got a job in a pet store, abusing and killing animals for the hell of it. Then he became a gambler, and then a crime lord, and by the time of the series, has plans to open a portal linking Demon World to the human realm just because "life would be more interesting" that way.
Even though Sakyo is still a sociopath, he remembers his happy childhood with a warm fondness, genuinely loved his family ("My parent were decent and kind people; it was what you could call an ideal family") and blamed nobody but himself for how he turned out, the English dub added a lot of changes to his narration, making him hate his parents and swearing he would kill himself if he became a white-collar worker.
Azusa from Hot Gimmick. Some have said that Ryoki qualifies as one, but he seems to be more of a Borderline, or perhaps Narcissistic Personality. Hatsumi, meanwhile, seems to have some traits of Dependent Personality Disorder. Actually, most of the characters are probably diagnosable with some sort of mental illness or personality disorder.
Due to a car accident and resulting brain damage, including some brain removal during multiple surgeries, Kazuo Kiriyama of Battle Royale cannot form meaningful connections to anything (a condition known as pseudopsychopathy in real life). The manga shows him mastering painting and the violin... and immediately throwing out both his artwork and his instrument when he's finished with them. He only associates with his "friends" because they won a coin toss; when they lose a second coin toss on the island, he slaughters them.
Interestingly, he is VERY self-aware that he is a sociopath. One of his lines, is that he sometimes gets 'confused' on right and wrong. When he slaughters his friends, he takes no pleasure in it. It is just something he has to do. Afterwards, however, he becomes a Determinator, dedicated to winning, with few lines.
Kazuo seems more of a Schizoid than an actual Sociopath. Sure he doesn't have a set moral compass but it's not because he doesn't like following the rules, he just doesn't care. He's never had a close friend (aside from his gang which he barely hung out with) and is completely indifferent to the circumstances surrounding him (such as when Mitsuko tried to flirt with him, but ended up getting herself killed instead.)
Let Dai: Dai doesn't understand empathy or why Jaehee cares about anyone other than Dai and himself.
In the FMA manga and Brotherhood anime, Envy, Pride, Shou Tucker, and Kimblee are this as well. This version of Kimblee is a particularly chilling example of high-functioning sociopathy, being an extremely intelligent, extremely self-aware psychopath in the vein of Hannibal Lecter, masking his lunacy beneath a Faux Affably Evil facade and a bizarre code of honor.
Agon Kongo of Eyeshield 21 is this, along with having every single trait that characterizes antisocial personality disorder. Fortunately, with the series' scope being limited to high school football and a shonen jump title, most of his truly horrendous acts are stopped before they could follow through.
Lloyd from Code Geass cheerfully refers to himself as a sociopath. An odd version in that he's not really a villainous character; he's very indifferent to all the fighting, manipulating, and killing that goes on around him, but really all he wants to do is fiddle around with the latest high-tech gizmos For Science!. There are Alternate Character Interpretations, though, such as Ambiguously Disordered.
A true sociopathic character from the same anime is Brittanian knight Lucciano Bradley.
Prince Schneizel is an Affably Evil version. Lelouch points out towards the end of the show that Schneizel's inability to care about other people turns out to be his Achilles heel.
From Naruto we have Hidan, who unlike most characters in the series has no positive traits and never did. He slaughtered his village simply because he was disgusted with their pacifistic way of life, and performed gruesome rituals to attain immortality for himself. He's also Axe Crazy and cruel for its own sake. On top of that, even the series itself seems to posit him as the most unsympathetic major villain, as he's exempt from the Cycle of RevengeAesop pervading the storyline with his Fate Worse Than Death (though it helps Shikamaru's case that Hidan has nobody who would care about his cruel fate barring potential allies, and also that just killing him would be impossible).
Both ROOT and the Bloody Mist era of Kirigakure were dedicated into turning their shinobi into merciless killing machines without any emotions or who knew right from wrong. Sai, a member of ROOT who becomes a member of Team Kakashi claims the practice of killing the people closest to them is discontinued, but honestly struggles most of the story with dealing with emotions, figuring out what is right or wrong, and basic social interaction due to his training.
Big Bad Naraku from InuYasha. As a conglomerate consciousness nothing about Naraku's psychology is normal, but he loves to manipulate people, play with their feelings and/or corrupt them, using them and later discarding them, without any remorse whatsoever.
Medaka Box: A lot of the characters are sociopaths to some degree (the title character narrowly escaped becoming one herself), but Ajimu takes the cake: not only does she regard people as things she's a Physical God. There's also Shiranui, who pitted her friends against an Irish wolfhound (a giant dog that was used to hunt wolves in Ireland) because it was funny.
However, it becomes clear that he isn't a complete sociopath when we learn about his past and realize that there is at least one person he cares for - Shinra. It's so extreme that he's more or less Yandere for him (though not in the romantic sense) to the point that he's stalking the man who hurt Shinra and setting him up for two huge crimes even though he realizes that he could get into trouble too. He even gets close to breaking down at the thought that he might have to betray his only friend to advance in his own goal.
Also, Izaya's never said that he is unable to love, just that he simply has no desire to.
Sosuke Aizen from Bleach. He puts on an affable façade, is themost manipulative character in the manga (with the possible exception of Kisuke Urahara), sees people as little more than pawns and tosses them aside once they've outlived their uselessness, harms people just because he can (just look at what he made Hitsugaya do to Momo), and tortured and killed who knows how many shinigami in order to create the Hogyoku, just so he could 'stand in Heaven'. He's responsible for the creation and near-execution of the Vizards, and came pretty close to destroying Soul Society itself. Mayuri has sociopathic tendencies as well, given the lengths he goes to in the name of 'research'.
Mayuri is definitely a sociopath. As his "evil-counterpart" on the villain's team, Szayel Apporo Granz, and quite a few other Arrancar, and by definition all normal Hollows. That some Arrancar aren't this is actually the remarkable part, but plenty of them aren't, even among the total bastards.
Nnoitra Jiruga and Kenpachi Zaraki also count.
Kenpachi is spared from being a total sociopath since he has at least three Morality Pets, including his adopted daughter Yachiru. If he were a true sociopath it's unlikely he would have bothered to spare her life, much less raise her and make her his squad lieutenant.
Incredibly, another contender has come along, with none of the Affably Evil of either, yet the A God Am I mentality of Aizen: Giriko Kutsuzawa. He kills his wife to test his ability.
Current Big Bad Yhwach is this. He treats everyone as pawns and as things to be replaced, seems to be warring against Soul Society since its there (not due to the old Quincy Genocide which probably a lot of his followers joined up to enact revenge for), reacts with zero emotion when he kills most of the 'impure' Quincy when his powers return, and doesn't care if the Vandenreich tears itself apart when he names Uryu Ishida as his successor.
As well as completely disregarding human feelings, which doesn't really count since he hates them, he mindslaves his psychic 'sisters' into a giant million winged angel without really noticing they didn't want to, and torments his twin brother.
Nakago in Fushigi Yuugi will go to any means to achieve his goal of godhood, and manipulates anyone who can advance his goals, and kills them when they are of no use to him. He manipulates Yui into making him a god, and knows that she would be eaten by Seiryuu after wards, and kills one of the Seiryu warriors when he has no other need of him.
Hody Jones from One Piece; Fukaboshi's description of him fits the definition, as he's done many horrible things including revoking the prejudice of humans by assassinating the queen and blaming it on a human he had hired to work for him only to betray him and later taking over the kingdom and killing anyone who got in his way.
Since it's a manga about pirates, One Piece is full of sociopaths. Blackbeard, Doflamingo, Kuro, Morgan, Krieg, Arlong, Spandam, etc... It's actually harder to find a villainous character who's NOT a sociopath than one who is.
Despite somefan objection, this sums up Griffith from Berserk. His high intelligence and charismatic and charming nature allows him to be quite ruthless behind closed doors, and he's fully aware of any line that he crosses so long as it brings him closer to his goal. Funny thing is that his counterpart, Guts, is himself a bit of a psychopath, but he has a working moral compass that prevents him from going that extra mile of no return.
Though there's plenty of Axe Crazy to go around in Baccano!, there is so far only one canonically confirmed sociopath is revealed in Children of the Bottle. Against all odds, this is not the unrepentantly callous Huey Laforet (who is capable of truly caring for a smallfew) or even the gleefully sadistic Fermet (who can understand and experience strong, genuine emotion), but rather the unrelentingly optimistic Elmer C. Albatross.
Mobile Suit Zeta Gundam has Sociopathic Soldier Yazan Gable, a thuggish Blood Knight who admits that he only joined the army so that he could legally kill and injure people. Willing to kill superiors whom he disagrees with, and loyal only to those he considers stronger than him, Yazan's a low-functioning sociopath who has managed to find his niche in the world.
Mobile Suit Gundam ZZ has Glemmy Toto, a superficially charming and affable young man, who views everybody around him as a means to an end. He treats Leina and his army of Puru clones as tools to be discarded at will, becomes stalkerishly obsessed with Roux after meeting her once, and demonstrates no loyalty whatsoever to any of his superior officers. The series also includes Rakan Dahkaran, a higher-functioning Yazan expy who fights for whoever seems strongest, and is willing to do any job, no matter how vile, if ordered to.
Katejina Loos, of Victory Gundam, is an interesting Character Development example. She starts out as one of the heroic main cast with Uso. However, even then, you could see signs of her true nature rising to the surface. After she is captured by the Empire, she charms her way into joining the BESPA and manipulates everyone else around her. She then turns against the Federation Forces and tries to kill Uso on multiple occasions. She kills off five of the established cast members. She does all this to fuel her own ego and to take advantage of any situation given to her.
Mobile Fighter G Gundam has a high-functioning example with Prime Minister Wong, ruler of Neo Hong Kong and. Not content with ruling through Gundam Fight victories, Wong plots to make his control over Earth and space permanent by using the Devil Gundam. He forms a Big Bad Duumvirate with Master Asia, but he has no respect for Master Asia's philosophies nor interest in his own motivation. Wong will happily manipulate him along with everyone else and gloats with laughter when a coughing fit prevents Master Asia from attacking him. Wong makes no effort to understand the motivations of the fighters either and is often confused or bored by their passionate behavior while he shamelessly tries to rig their matches. He kidnaps Allenby to make her the Devil Gundam's pilot and discards Master Asia as soon as his plans are advanced enough.
Mobile Suit Gundam 00 has Yazan expy and Psycho for Hire Ali Al-Saachez, who will do anything if the price is right, enjoys violence for its own sake, and can't keep up the facade of being an actual human being for more than a few moments at a time. He once used religious rhetoric to create an army of child soldiers and got them to murder their own parents, despite the fact that he himself has no belief in God. Why? Somebody paid him to do it. He cheerfully describes himself as the worst kind of human being.
Mobile Suit Gundam AGE has sociopathic child soldier Decil Galette, who views his own troops and his enemies as toys in a game he's playing. As an adult he persists in this attitude, and is absolutely hated by his own side for the way that his egoism and Lack of Empathy impact their efforts. As a child commander, he retreats from a winning battle out of boredom. He holds a mutual grudge against protagonist Flit; on Flit's end, it's for killing a Love Interest. Decil is just as angry... over the fact that Flit beat him up for doing so. As an adult, Decil's psychic powers aren't as unique an asset, as his brother is promoted over him and Decil is treated as an Elite Mook with the more-numerous X-Rounders of Generation 2. He routinely breaks formation to fulfill his grudge against Flit but his ego far outweighs his abilities. Finally, when he starts using his allies as Cannon Fodder again, Zeheart withdraws all support and allows Asemu Asuno to kill him.
Kayaba Akihiko, the Big Bad of the first arc of Sword Art Online, is a surprisingly realistic sociopath. He clearly has trouble seeing people as people, and he built his death game not because he wanted thousands of people to suffer, but simply because he wanted to build a world, and it wouldn't have been real if it wasn't populated. Nothing he does has any malice in it, and he played by the same rules as everyone else, always intending for the game to end with his death. Kirito especially slowly gains a grudging respect for him, if only because it's hard to hate someone like that.
A straighter example is Nobuyuki Sugou, who high-jacks the minds of 300 of the SAO victims (including his then-fiance Asuna) and traps them in his own game ALFheim Online to experiment on them. Notably, he is a vicious Sadist as well, unlike Kayaba.
Ana Satsujin has Rio Miyaichi, who is a mostly unrepentant serial killer and also our main character's new girlfriend. While she claims to only kill criminals, she also makes it clear that she's perfectly capable of killing anybody she feels like, and at one point randomly kills a police officer for no apparent reason aside from simply not liking his tone of voice while he was questioning her about another killer (while she herself wasn't under direct suspicion at the moment), and justifies her actions by saying that cops aren't people.
Rize Kamishiro from Tokyo Ghoul appears to have been one. A beautiful young woman, she used charm and manipulation to lull victims into a sense of ease and then brutally killed them. Her appetite earned her the title "Binge Eater", for she frequently killed simply for the amusement while completely unconcerned about the consequences of her actions. Among Ghouls, she was infamous for moving into a Ward and throwing it into chaos with her sprees, then skipping town once her actions had brought in the authorities. If she had an ounce of empathy or compassion, she never showed it and stated she only cared about enjoying herself. Even other Ghouls found her selfish and cruel.
Silas Edwards and Allen from Mother Keeper are both this, Silas buys slaves, drugs them and forces them to fight to the death for people's amusement. Allen was a part of this and kidnapped the person closest to one of Silas' slaves and forced them to fight to the death.
Quite a few of the "targets" from Hell Girl portray sociopathic traits, most commonly by being almost unimaginably self-centered. A prime example would be a teenage baseball player who beats one of his teammates to death with a baseball bat and frames another for it...so he could get out of playing a game and putting strain on his shoulder.
Homura Akemi from Puella Magi Madoka Magica shows a few traits of a textbook psychopath, among traits of emotional abuse towards her target, Madoka Kaname. Read about it here.
Thanks to the Black And Black Morality, all the villains they face also fall under this. Hell, even Ciel's staff, normally the Plucky Comic Relief, turn out to be this trope when we find out the real reason Ciel hired them was their combat skills making them practically one-man armies.
Quattro from Magical Girl Lyrical Nanoha StrikerS took great pleasure in torturing Vivio, called Dieci stupid for being bothered by it, manipulated Vivio into a fight to the death with her mother Nanoha, felt the need to taunt Nanoha, and spent most of the final battle calling her enemies and allies worthless. The only point she doesn't hit is a lack of attachment, since she's loyal to Jail.
From Texhnolyze: the two main antagonists. Yoshii not only kickstarts a civil war in Lux, but murders a prostitute he had seemingly bonded and sympathized with the night before for no conceivable reason. Kano takes this trope and ramps it Up To Eleven, revealing in the final episode that not only does he have no problem forcefully turning a little girl into a cyborg, but that he doesn't even believe that anyone in Lux actually exists, let alone count as actual people.
Tokugawa Harusada of Ooku: The Inner Chambers, in her childhood, regularly lied, framed her sister for theft, later pushed her to her death, and poisoned her own mother, all because she was bored. Since becoming mother of the shogun, she's poisoned a maid, gotten a senior councilor fired for not giving her a title, pitted her son's wife and concubines against each other, and killed her own grandchildren, all for her own amusement, and because the glory of sitting at the pinnacle of power wore off.