Akagi 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.
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.
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.
Wyald is a far more low-functioning example than Griffith and Emperor Ganishka, as he is extremely impulsive and always pursuing instant gratification for himself with no respect for the lives or well-being of others, or even his own.
Bleach: In this series which features many characters of varying degrees of morality, the ones mentioned below stand out as having very little in the way of moral standards.
Mayuri Kurotschuchi introduces himself by blowing up his own subordinates, and then blowing up the one who didn't explode because "a bomb isn't supposed to come back". He then goes on to describe in horrific detail the experiments he carried out on the Quincies, right in front of Uryu. He's also heavily abusive towards his own daughter and creation, Nemu. He's sadistic, cruel, has no regard for others' safety and well-being, and only cares about something or someone if they pique his scientific interest, which is not a good thing. Despite all this however, it is shown that he does hold some degree of affection for Nemu, as he is shown to be distraught at her death.
Sosuke Aizen puts up an affable facade to gain the trust of others. He is highly charismatic and manipulative. Aizen sees everyone around him, including his underlings, as little more than pawns to use and dispose of, has no empathy whatsoever, harms people just because he can, and tortured and killed who knows how many soul reapers in order to create the Hogyoku. He is unbound by any form of honor, law, morality, or decency, and is driven by a desire to 'stand in heaven'. When invading Soul Society in the Deicide arc, Aizen carelessly walks through Karakura knowing that anyone who came into close contact with his Reiatsu would die, showing no emotion while doing so, and played a twisted game of cat and mouse with Ichigo's human friends with intent of killing them and stringing up their corpses just to see Ichigo's reaction.
Nnoitra Gilga believes that Hollows are damned souls who shouldn't bother with things like "redemption" or trying to better themselves, and thus he sees nothing wrong with trying to kill anyone and everyone in his path as he seeks to become either the strongest around or gets killed in battle by someone stronger, both of which he longs for. He loathes Nel because she pitied him, and attempted to kill her and her Fraccion to achieve a higher rank in the Espada. He savagely attacks Ichigo, breaking his arm, and forces Orihime to watch Tesla give a No-Holds-Barred Beatdown to Ichigo, taking sadistic glee in their anguish. Even Ulquiorra, who is incapable of feeling emotions is disgusted with him. The only person he's ever shown a smidgen of care for is his Fraccion Tesla.
Grimmjow Jaegerjaques believes that he is destined to become the king of Hollows and that anyone else is either a stepping stone or obstacle to get rid of, a follower who will serve him in reaching that point, or a rival that needs to be put down for getting between him and that goal. When his loyal Fraccion are all killed, he shrugs off their deaths rather easily and shows more anger about how his reckless actions got his arm chopped off and kicked off the Espada as punishment. As soon as Orihime heals his arm, he gleefully kills Luppi by impaling him through the torso and obliterating his upper body with a Cero. While he works for Aizen, he holds no loyalty to him beyond the fact that he isn't strong enough to take Aizen down, which greatly irritates him. He goes against orders on a number of occasions, and saves Orihime from Loly and Menoly only so that she can heal Ichigo so that he can have his showdown with him.
Szayelaporro Granz sees nothing wrong with turning his own Fraccion into edible food sources to heal his injuries, nor does he see anything wrong with sacrificing someone else in order to use his Gabriel technique. When Renji assumes that he wants to avenge his brother Ylfordt, he laughs off the notion as to him, losing his brother would cause the same emotional reaction as to losing a box.
Shukuro Tsukishima's major focus seems to be on Ginjo to whom he has Undying Loyalty. However, it's implied he does care about Riruka as well since he was horrified he injured her. Despite those cases, he doesn't seem to care about anyone else. Tsukishima uses Book of the End on Ichigo's friends and sister to psychologically torment him. When Orihime and Sado start to break free from his control, Tsukishima messes with their heads for no apparent reason before he is stopped by Ginjo. It's implied that he has permanently broken many people's minds in the past. He's not just willing to break the minds of people but he thoroughly enjoys doing so.
Yukio Hans Voralberna bemuses at Jackie Taking the Bullet for Renji, boasted that he drove his father to suicide, and completely fine with the prospect of Riruka dying. Subverted after everything is over and said boasts are revealed to be a mask that hides the fact he can't deal with his feelings due to said events.
Giriko Kutsuzawa has no real regard for human life. His way of testing his powers was killing his wife. The trope was enforced by said ability when it made his eye explode for feeling bad about it.
The final Big Bad, Yhwach, is an incredibly ruthless and brutal psychopath who Yamamoto states has no compassion for anyone, not even his own men. Yhwach will not let anyone stand in his way and will cross as many lines as he feels is necessary to accomplish his goals without hesitation. Six years prior to the start of the series, Yhwach strengthens himself by using Auswählen, taking the powers of any Quincies he deemed "impure" or "unnecessary", including children, resulting in their deaths, showing no remorse for this act. Yhwach is also quite prone to violence, lopping off the arm of an Arrancar just to get his attention, and kills several Soul Reapers, Arrancar and Quincies alike in a calm and serene manner. When performing Auswählen for a second time on the Sternritter he left behind in Seireitei to revive the Schutzstaffel, Liltotto demands to know what the Sternritter were to him, and Yhwach replies that they are comrades helping him. Yhwach sees nothing wrong with sacrificing his own soldiers to empower himself, and expresses confusion at Ichigo's anger at the death of his mother, who was a victim of the first Auswählen, because in Yhwach's point of view, there is no greater honor than empowering him. He's also quite self-centered, outright stating that everything in the world exists for his taking, and can be pretty sadistic at times.
Tokinada Tsunayashiro, from Bleach: Can't Fear Your Own World, is a smug, arrogant, self-entitled, sadistic asshole who indulges his cruellest whims out of the belief that Soul Society is built on a foundation of lies.
Candy's bitchy step-sister Eliza Reagan in Candy Candy has several sociopathic traits. She's wholly selfish and incredibly manipulative, feels no shame in hurting others for her own gain or amusement, and believes she's entitled to get whatever she wants, by any means necessary. Never in the whole series does she ever show any sign of caring for anyone other than herself - even her Villainous Crush on Terence was less about caring for him, and more about wanting a hot guy all to herself.
Her brother Neil is no better - not only is he just as selfish and uncaring about hurting other people, but toward the end of the series, he develops a Villainous Crush on Candy, and it's just as shallow and selfish as Eliza's on Terence, not to mention obsessive to the point where he attempts to lock her in a house and never release her until she agreed to be his lover.
Lloyd Asplund cheerfully refers to himself as a sociopath. However, he could be considered a subversion since he actually lacks many of the symptoms of true sociopathy (Lack of Empathy, chronic lying, and narcissism); he's just very indifferent to all the fighting, manipulating, and killing that goes on around him, and all he really wants to do is fiddle around with the latest high-tech gizmos For Science!.
A true sociopathic character from the same anime is Britannian Knight Luciano 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.
Vicious from Cowboy Bebop. Vicious is a cold, ruthless, bloodthirsty, and ambitious man who prefers solitude. He's Chronic Backstabbing Disorder incarnate, ungrateful to everyone, even if that person gave their life to save his ass. He's also willing to sacrifice anyone to further his own goals, weather it be his men, mentor, or even his loyal bird. The only thing he seems to really care about is power and revenge.
Death Note: Light Yagami, the Villain Protagonist, is a particularly interesting example, since Light acquires sociopathic/psychopathic characteristics when the notebook controls his life. invokedWord of God has explicitly stated that Light was not born evil or heartless, after all. However, as soon as the notebook controls his life and gets into the habit of killing people, he exhibits all the characteristics of a highly-functional sociopath: he displays highly developed social skills, is exceptionally adept at gaining the trust of relatively naive and/or stupid people (superficial charm), has an inordinate self-worth to such a degree to believe that he is a God and an excellent person, gets bored easily, frequently lies and cheats to achieve his goals, frequently manipulates and betrays; He lacks mostly empathy; He pretends to have feelings for Misa to manipulate her emotionally, tends to throw a tantrum or physically attack people when things are not going his way, and is controlling and possessive. Even Light's plan to establish a utopia is an absurdly childish and unrealistic goal, which is common for sociopaths to have unrealistic goals.
His minion Doma also qualify. In Chapter 157 Kanao calls Doma out for all his attempts at emotion being farcical. Doma feels no emotions and can't feel them to where Kanae states she would feel sorry for him if she did not hate him so much. He's so detached that even while beheaded and dying, he doesn't really feel anything and doesn't mind.
Izaku from Eternal Sabbath is an Artificial Human born with Psychic Powers that enables him to read and control other people's minds. Believing himself to be a genetically perfect being and superior to normal humans in every way, he uses his abilities to make people kill each other and/or themselves. He befriends a little girl, Yuri, and he helps her kill those she considers "bad people", but he also kills anyone who interferes with his plans, including a kind-hearted police detective who is suspicious about him. When Yuri begins to question his methods, Izaku kills her without a second thought by making her hallucinate about her mother (whom he already killed beforehand). Later, he discovers that he is dying, so he begins a rampage in the city and causing numerous death and destruction of property because bringing such chaos is the only thing that gives him any semblance of satisfaction.
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.
Solf J. Kimblee is a very nasty, low-functioning sociopath. He's only in the army for the chance to kill people, and takes it well beyond even the most Sociopathic Soldier. He doesn't even have any real loyalty in him; he just likes to hurt people. He had no qualms blowing anyone up, even innocent Ishbalan civilians. This extends to women and children.
Solf J. Kimblee is a high-functioning and very self-aware psychopath with a decidedly unusual worldview. For all his sadism and disregard for human life, he does have some honor - largely based on honesty and duty and abides seriously by it, to the point where he genuinely respects anyone who can consistently adhere to their own moral/professional codes, even those wholly opposed to his own. Indeed, by the end, he considers his own existence expendable, opting to distract Pride and subsequently have his own soul vanish rather than "live" inside of a hypocritical homunculus.
Father, a being who manipulated a king into destroying his own country so he could become immortal, then spent the next centuries creating a military dictatorship so that he could destroy that country to become God. He has no emotions because he cast them off into the Homunculi, and genuinely sees humans like they see ants.
The King of Xerxes, who was perfectly willing to go along with Father's plan to slaughter his people for immortality.
Barry the Chopper, a butcher who became a Serial Killer because he loved chopping meat that much, and saw his soul being bound into armour as an opportunity to kill more people.
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 afterwards, and kills one of the Seiryu warriors when he has no other need of him.
Goblin Slayer provides a remarkably textbook example that encompasses an entire race. The goblins are born without any empathy or ability to self-reflect; they do not, will not, and more importantly cannot recognize the pain they inflict on their victims. They see themselves as the superior race against common sense, and feed into that sense of superiority by degrading others through deception and assault. At the same time, they are blind as to why some people would hunt them down as a result, instead vowing to continue raping and murdering as revenge for something that was their own fault to begin with. Not that goblins need much more motivation anyway, because their short-term thinking and inability to delay gratification means they will almost never pursue anything beyond their destructive impulses. They don't even care for their own brethren, backstabbing and abuse being commonplace within their ranks. Most damningly, like any cornered sociopath they will default to cheap sympathy-ploys akin to slipping a mask on - there's no genuine sorrow present, just the hope that someone falls for their lies. The rank and file goblins act like low functioning sociopaths, while the smarter and more cunning classes of goblins act like high functioning ones.
The Manager of the Princess Imperial is initially presented as a gentle and caring boss, but hides a bloated sense of importance that cannot abide seeing others being more loved than she is. When Mitsuboshi asked Satou out on a date, she responded by kidnapping and raping him for a week as a way of rectifying that, while manipulating everyone else to bully Satou and making her work extra shifts with no pay. When Satou confronts her about this, she quickly tries to pass of the blame on Satou (for stealing attention from her) and Mitsuboshi (for falling in love with Satou), claiming that they "ruined" her empire.
Asahi's father is a low functioning example of a sociopath who wastes no time with wasting the money he received from his inheritance after his father's death to spend it on his hedonism. He lacks empathy for anyone he hurts, having raped his wife when they first met after she accidentally bumped into him.
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.
The Major from Hellsing is a classic sociopath. The Major is charismatic, manipulative, and wickedly intelligent, even through his batshit insanity, but is simultaneously utterly bloodthirsty and utterly devoid of anything remotely resembling empathy.
Miki Kirishima from Hideout is a self-serving woman who paints herself as a grieving mother when her son died in an accident, but later displays disinterest in having another child and even coldly admits that she never wanted a son to begin with.
There are many examples from Hunter × Hunter such as some of the Chimera Ant soldiers, and other characters fulfill some of the criteria such as the Phantom Troupe, but they don't exactly fit the mold of complete sociopaths as they actually care about one another, engaging is a hefty dose of hypocrisy, where they kill wantonly and without remorse, but become infuriated when one of their own is killed. The one character however, who fits the sociopath mold perfectly, is Hisoka. A man with a clown and magician theme, whose sole goal in life is to find strong opponents so that he may derive sexual pleasure from fighting, outsmarting, overpowering, and killing them. Everything he sees is viewed through the lens of whether or not they can stimulate and entertain him, as he spares absolutely no thought for regular people, and will kill those who disappoint him in combat without remorse. He has at times killed solely to satiate his bloodlust but exercises restraint at other points if he believes letting his opponent live will lead to them getting stronger, and thus, a greater fight and thrill for Hisoka himself. The fact that despite being in the series from the near beginning, he has never really changed his goals or mindset as well as his self serving goals makes Hisoka a darkly realistic depiction of a sociopath.
While her behavior is usually Played for Laughs, Tabane Shinonono in Infinite Stratos shows several traits of a sociopath: she does things and takes decisions (including but not limited to aiding a terrorist organization threaten the safety of society) on the basis of how much fun she gets out of them, consequences be damned; she has a grandiose ego and a need for it to be constantly fed; she cares about no one that isn't herself or her right-hand woman Chloe (it is often shown that despite her upbeat attitude, she is a very hard person to like); and she can be very manipulativewhen she puts her mind to it. Although she does seem to care about her sister Houki (who rather understandably dislikes her), Chiyufu and Ichika, she also has no qualms about endangering them as her whims dictate.
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.
The Goddess Ishtar has many traits of this. She's a malignant narcissist who commits heinous actions such as rape and torture without thinking twice and is willing to wage war over a petty grudge. She also manipulates the members of her familia into doing what she wants, seeing them only as tools to bolster her own power, even literally since she commonly has Human Sacrifice rituals to give herself a power-up. And she is incapable of accepting any responsibility for her shortcomings, including wondering why people hate her even though all her misdeeds are common knowledge.
Her captain, Phryne Jamil, isn't far behind, though she is more low-functioning. She's a Torture Technician and Serial Rapist who sees nothing wrong with what she does to the men that she "tastes," believing that they enjoy her and aren't traumatized by it. She's arrogant to the point of delusion, seeing herself as the most beautiful woman in the world when the exact opposite is true. And her true violent tendencies show when she is in battle, thoroughly enjoying the slaughter.
Itsuwaribito has Gin Hobaku, the itsuwaribito who killed Utsuho's family in the past. A twisted sadist who enjoys using his charisma and intellect to gain other people's trust and manipulating them to do his bidding before callously betraying and killing them for his own amusement, he's built a reputation as a local hero and turns the entire town (and their army) against the heroes when Utsuho attacks him. When one of the royal guards starts suspecting him and goes digging around his room for evidence of wrongdoing, he takes his time toying with the man with shallow cuts and poison, before trapping him in a secret underground tunnel to make his body disappear. Later, when the man's nephew tries to confront Hobaku for his evil deeds, he hires thugs to attack the palace and pretend to be the former's underlings to frame the young man for treason. He later acknowledges that he could use his great talents to be a real hero, but thinks that he'd be getting the shorter end of the stick in doing so, since those other, lowly people can't benefit him the way he could benefit them—and, besides, where's the fun in that?
His minion Telence T. D'Arby exhibits many typical traits of a textbook sociopath, including a Lack of Empathy and manipulative nature. Kakyoin even calls him one in the English dub.
Yoshikage Kira, who has an Ambiguous Disorder that gives him the drive to murder. He knows that killing people is wrong, but he sees it as a bad habit rather than an amoral crime. While he prefers not to fight, he does so out of a need to protect his own identity, and will not give his victims a peaceful death. As Kosaku Kawajiri, he scares, emotionally abuses, and outright kills his "son" Hayato, and he's brought back to life, he turns him into a literal Tyke Bomb so anyone who asks him for Kira's real identity will painfully die over and over.
To drive this point even further, his fight against Stray Cat, in which his wife, or better put: the wife of the man he stole the identity from, gets injured from the attack. He instinctively shows worry for her, and tries to shield her. When he realizes he's starting to show a slight bit of empathy towards another person, he immediately refuses the call to Character Development and states in his inner monologue how someone like him only protects people when they're convienient.
And then there's Diavolo, whose introduction to Part 5 is dismembering a traitor to his gang, an act so gory the other traitor he had caught committed suicide. His defining trait is his extreme paranoia, preferring to run everything from the shadows and killing everyone that finds out his true identity. This trait is firmly established when it's revealed that he burned his hometown down, with the intent of being among the listed casualties. His other defining trait is his Lack of Empathy; he shows no remorse towards anyone, not even his split personality, and upon finding out he has a daughter, he has her sent to him with the intent of killing her, never mind the fact that, up until that point, she had no idea who he was, simply because he couldn't accept the chance that she might know.
The Kindaichi Case Files has Yoichi Takato, a Serial Killer who sees crime as a form of "art", and gleefully commits murders, or helps other people commit murder, for the sake of his "art" without any concern for the lives lost in the process. Oftentimes, he'd also enlist Kindaichi (and sometimes Akechi as well) because they're some of the very few people who can match his intellect and would be able to solve the mysteries he craft, as though the murders he committed are just a sick game hide and seek. He's quite a skilled actor too, being able to act as a clumsy, timid manager of a magician's troupe in the first case he's introduced in.
Kill la Kill: Ragyo Kiryuin shows multiple signs of sociopathy, possessing an extreme sense of self worth and ego and a total lack of concern about her offspring to the point of sexually abusing her elder daughter Satsuki and literally throwing her younger daughter Ryuko away in the trash when the latter was an infant. She also ordered the death of her husband, casually sacrifices her employees and innocent bystanders to further her goals and outright rejects the concept of having empathy for anyone else. Her Leitmotif "Blumenkranz" outlines her thought process by comparing people to dead flowers that have to be trimmed without any remorse.
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.
Phil Maxwell in Magical Girl Lyrical Nanoha Detonation. Once the funding for the Eltria Reclamation project was cut he immediately had everyone murdered by Iris Units without even blinking an eye on the grounds that he was doing them a favor so that they wouldn't be assigned to more boring work. When Yuri confronts him he admits that he never loved Iris or anyone else; he just pretended he did because it produced results. And finally he has no problem destroying Earth, all in the name of profit, despite the billions of people living there.
Magical × Miracle has Ardi, a wizard from a distant country who traipses into Viegald and immediately puts half of the population, including the King, under mind control. As a child, he hit girl who tried to profess her love for him, and laughed at her tears. He also killed a fortune-teller and felt no remorse. And his motive for trying to take over Viegald? He wants to kill the famed Master Wizard of the land, whom he believes to be the only other magic wielder whose powers rival his own.
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.
Johan Liebert, the titular character from Monster. Any description of his sociopathy would become a plot summary.
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.
All For One carries all the traits of a classic sociopath: He has no empathy or remorse for all the things he has done, shamelessly bragging to his brother about how his followers had wiped out a faction of Quirk users who refused to join him. He views others as mere pawns to be used. He lies and manipulates others with ease. He's a Sadist who enjoys getting under other people's skin, often taunting All Might about the death of his mentor. He is incredibly arrogant and condescending to the point of megalomania and is charismatic enough to gain a loyal following of villains to serve under him. Even his taking in Tomura as his apprentice wasn't done out of altruism, but as a means of getting back at All Might by grooming Nana Shimura's grandson to be his successor.
All for One: [in response to a Heroic Sacrifice] Thank you for such wonderful comedy!
Kai Chisaki, otherwise known as Overhaul, the main villain of the Shie Hassaikai Arc. He is ruthless, manipulative, and views others as a means to an end especially with Eri whom he repeatedly uses his Quirk on to break her down and use her blood and cells to create bullets that disable a user's Quirk. He even has the ability to "resurrect" people after dismantling them once doing it to another villain five times. While he believes himself to be well-intentioned and cares for his former boss, this did nothing to deter him from putting his boss into a coma when his boss was appalled with his experimentation of Eri.
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 bloodthirsty 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).
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.
Three of the four Vinsmoke brothers the exception being Sanji definitely qualify. They have a severe Lack of Empathy, using their cloned soldiers as human shields and casually abusing servants. They're also almost completely emotionless, to the point at which when they, their sister and their father are about to be killed, they simply laugh and joke about it, not caring for their own lives or each other's.
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.
Shogo Makishima of Psycho-Pass is a charming, intelligent man who always has a bright white hue when analyzed by the Sibyl System's sanity detectors, even as he's slitting a girl's throat. Makishima also encourages other people to become serial killers and only views them as tools to be abandoned once they stop entertaining him.
More prevalent are the masterminds behind the Sibyl System, the Wetware CPU consisting of 'criminally asymptomatic' brainsnote they are hard-wired to commit criminal acts but can hide their true personality from society. Sociopathy is literally a requirement to be recruited into their ranks, as they explicitly recruit from criminals who have a strong enough façade to fool the system; the only reason they don't hire Makishima is because he wants everyone to know what he has done.
Maria "Ai" Imari is a researcher who creates a strand of the Pupa Virus solely to impregnate herself with it so she could birth a monster. She suggests that Utsutsu become Yume's meal due to his regenerative abilities, but she otherwise expresses no concern if Yume were to transform into a monster and go on a ravenous rampage. She also remorselessly assimilates Yume to complete her goal.
Genjurou Imari was Maria's grandfather who had the tendency of adopting orphan boys and then savagely torturing them for his art. He also psychologically warps Shiro's mind into believing that such violence was love.
Redo of Healer: The Kingdom of Jioral has several up to and including:
Flare; prior to her being brainwashed and becoming "Freia," would physically and sexually abuse Keyaru to force him to use his healing power and if that didn't work, she would use drugs to make him more susceptible. The Kingdom doesn't see this side of her due to being superficially charming.
Her little sister Norn is even worse before also being brainwashed and becoming "Ellen". She had multiple "toys" that she abused for her own enjoyment. Once she got bored with them, they were discarded. She's also a manipulative warmonger who sees no problem with using violence and bloodshed to get what she wants.
The "heroes" Blade and Bullet: Blade is a Serial Rapist of women who would slip aphrodisiacs into their drinks and then take them to have her way with them. She is superficially charming to the girls she fancies, yet she only sees them as conquests as evidenced when one of the fathers of her victims approached her for revenge and she couldn't remember which one he was referring to. She also has a huge ego, taking offense at a disguised Keyaru bruising her "beautiful face." As for Bullet, he tries to pass himself off as a "Good Shepherd" to mask his shotacon fascination, and also sexually abused Keyaru.
Renard, the captain of Jioral's royal guard, had a sick love of raping women and giddily gloats to Keyaru about raping Anna all night.
Region: Takada sacrifices his students to the rats to save his own skin and later condemns hundreds of civilians to become rat food after his plan of disposing of his remaining student failed.
Rent-A-Girlfriend: Mami was the ex-girlfriend of Kazuya who dumps him in less than a month. She manipulates his emotions all while bad-mouthing him in public. Upon learning about Chizuru, she makes an attempt to "break them up" not because she wants to be with Kazuya again, but because she was enraged to see that he seemingly moved on after their breakup.
Revolutionary Girl Utena: Akio Ohtori has a superficial charm, which he uses to hide his despicable nature under the guise of a charming gentleman from the public. He manipulates everyone around him, including Anthy and Kanae, as pawns to regain his lost power as Prince Dios by any means necessary. He is a textbook Domestic Abuser to Anthy, passing her around like the prize to whoever wins the dueling game, raping her weekly, and telling her that only he can love her. He never accepts responsibility for Anthy's original death, her continued suffering, or his statutory rape of Utena; he instead puts the blame on both of them, the world, the townspeople, even claiming that Anthy willingly continued being a Silent Scapegoat for him and that Utena is guilty of sleeping with an engaged man.
Rosario + Vampire: Gyokuro Shuzen is completely incapable of caring about anyone but herself. Children by blood or adoption, lovers, subordinates... all of them are nothing but stepping stones to her and her quest for power and dominance.
In The Saga of Tanya the Evil we have the titular character herself, who has virtually zero empathy for others and makes no acts of kindness that aren't meant to further her own career in some way; the few moral conflicts she has in the light novel have minimal impact on her actions and are cut entirely from the manga and anime. She casually sends upstart soldiers under her command to their death without a second thought, and tries using her childish demeanor to guilt trip and manipulate a captain into retiring early to eliminate him as a competitor. Everything she does comes back to her goal of climbing the ranks and landing herself in a safe rear-line position, and she never looks back on her actions with remorse. Interestingly, this and the fact that her mindset effectively comes from almost a century ahead of the setting also result in constant miscommunications and misinterpreting the actions of others.
While the visual novel version of Makoto Itou could change alignments based on player choices, the anime adaptation of School Days very firmly establishes him as a high-functioning sociopath. He has a need for stimulation that he satisfies by attracting and sleeping with his classmates, even though he's already in a relationship with Kotonoha. He has enough superficial charm and deceit to present himself as an upstanding student and Nice Guy as well as conceal his sleeping around. He shows no lasting regret for the damage he causes, save Kotonoha, and even then only when she's in his immediate presence.
Medusa from Soul Eater proves to be a Consummate Liar who doesn't care about anyone else and has a charming facade that allows her to infiltrate the DWMA as a school nurse without anyone suspecting her before revealing her true colors. She. Her child, Crona, gets the worst of it (with the dub even having her call Crona "it" because of another trope) and she once locked Crona up when s/he was little in a dark closet with no food for 5 days when s/he refused to kill 3 rabbits in 3 different ways and subjected him/her to horrific experiments to make him/her a Humanoid Abomination.
Kayaba Akihiko, the Big Bad of Aincrad, 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, Fairy Dance's Big Bad, wanting to perform inhumane mind control experiments on 300 SAO survivors, whom he openly describes as "guinea pigs" rather than people, and making an incapacitated Kirito watch as he tries to rape Asuna without a flicker of remorse. Sugou also has a grandiose sense of self-worth, declaring himself a god and believing that he's entitled to have Asuna despite the fact that she can't stand him, and unlike Kayaba, he's a vicious sadist who revels in his cruelty and evil. He's a high-functioning sociopath, hiding his true nature to Asuna's father by playing the part of a friendly, polite Honest Corporate Executive.
Vassago Casals/PoH is among the darker, more dangerous depictions of sociopathy. He is misanthropic, bloodthirsty, manipulative, and utterly devoted to dog-kicking. He establishes the Laughing Coffin guild so he can have people kill each other to satisfy his bloodlust, and even corrupts many an SAO player into player killers and even real-life serial killers.
Quinella, the Administrator, the initial Big Bad of the Alicization arc. She never cares for the welfare of the UW people because it's all about her in her head. Justifiedin that she had to seal her emotions to prevent Cardinal from making her kill herself during times of emotional distress... but also double-subverted in that Quinella had already begun her experiments into manipulating the UW residents by this time, so she already was a psycho, she just made herself worse. She feels no remorse for the trouble she's caused and even convinces her victims that she's helping them by twisting their feelings and memories.
Gabriel Miller, the final Big Bad of Alicization, is a classic sociopath, and the most dangerous example in the series. He is charismatic, manipulative, and wickedly intelligent, even through his batshit insanity, but is simultaneously utterly bloodthirsty and utterly devoid of anything remotely resembling empathy.
Yuuka is revealed to have been a stalker obsessed with Shinji and was the one who started the fire at the movie theater concluding that she could make him her boyfriend by bringing him back as a zombie.
Tsuruoka is revealed to have established a child soldier program and places Nana into it after killing her parents. Despite claiming to be doing things out of her best interest, he truly views her as a useful pawn and had no qualms with ordering her killed for her insolence. He also promises her that he would help Michiru after she used up her life force to save her only to shoot her in the head two times to prevent Michiru from healing herself.
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.
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.
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.
Ami Kirio appears to be a weak demon boy who befriends Iruma and his friends but is in truth a manipulative sadomasochist who got off on despair whether it be others or his own. He conspired with Baal to trap the student body with his barrier magic the ultimate plan being to detonate a bomb to kill all the students and in that ensuing chaos, the students' families would be driven back to their primal states. Ami explains to Iruma that he became aware of his sadomasochism when he was sent to a rehabilitation school due to his low magical abilities and it was there he befriended a girl who loaned him her prized earring. When he accidentally destroyed it when trying to retrieve it from two bullies, he got a nosebleed from the sight of his former friend's grieving face.
Baal, one of the Thirteen Crowns of the Netherworld who had grown bored with the current state of the Netherworld and masterminded the attempted bombing of the demon school so that it would send the Netherworld back to its days of chaos.
Yakitate!! Japan has Yukino Azusugawa, the eldest daughter of Sadamichi Azusugawa, who is by far the nastiest character in the series.
She is a heartless woman who is implied to have murdered people to get her way. During the Rookie Tournament arc, she manipulates a Pantasia staff to sabotage Kawachi's bread and later murders the guy to cover up her involvement. A later bonus chapter flashback shows that she had attempted to kill Tsukino by pushing her into a well when they were both children, and Tsukino would have died of not for Azuma's bread.
She is a skilled actor, and can act like a kind—if eccentric—woman in public. Yukino had horribly mistreated Tsukino in the past, and still loathes her half-sister in the present; but when they reunite, Yukino is able to put up a friendly facade in front of her friends, and even fakes tears of remorse when they call her out on her past abuse towards Tsukino. Later on, while talking to her grandfather—the current CEO of Pantasia—she manages to pretend giving her support for Tsukino to become the bakery's next successor, thus convincing the old man that she is a selfless and considerate woman.
She is as sadistic and promiscuous as can be shown in a Shonen manga. She often walks around in public wearing Dominatrix outfit, and one Omake strip actually shows her walking around nude. Fittingly, when she is transformed into air particles after losing a baking battle against Azuma, she is temporarily placed inside an inflatable sex doll.
She has no loyalty to anyone, and later betrays her own family to join forces with Pantasia's greatest rival, St. Pierre. She seems to have an intimate relationship with the Big Bad owner of St. Pierre, but it's clear that their relationship is not born out of love, but their shared lust for monopoly and power.
Sakyou from Yu Yu 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.