Claire Stanfield (a.k.a. Vino) of Baccano! personifies the Unscrupulous of this.
Guts from Berserk has one goal in life: making his former ally Griffith pay in blood for what's happened to him. A childhood spent as a mercenary and an adult life spent being attacked by demons has left him with few moral precepts. He thinks nothing of cutting people in half, although he does prefer not to take out bystanders (still a bad idea to stand in his way, though). On the other hand, he cares deeply for Casca and has given some thought to what he really wants to do with his life once he's gotten his revenge; he doesn't have an answer for that one yet. Pre-Eclipse Guts is more of a Byronic Hero.
Mello is solely dedicated to being the one to stop Kira and is more than willing to become a mob boss, kidnap innocent girls, and in the manga, even threaten the President to sabotage his rival so said rival can't catch Kira.
Light's rival, L, is an Anti Hero and The Anti-Bishōnen. He dresses like a bum (he doesn't even wear shoes!), his black hair is shaggy and unkempt, he looks permanently hungover, he strongly detests physical contact with anyone and is close to emotionally dead. As far as his morality is concerned, he is willing to achieve the good goal of capturing Kira (Light) with evil means, such as kidnapping, not preventing murder, invasion of privacy and torture.
Hei from Darker Than Black. A hitman for The Syndicate who doesn't really bother to question the morality (or, more often, lack thereof) of his assignments, with no compunctions about cheating, killing, or torture if he feels it's necessary.
According to Akira Toriyama, in of the early series was originally supposed to be a selfish hero to the point that one wondered if he was actually a good person since he only grew stronger to fight strong people, not to protect anyone. Some of Goku's more heroic qualities were heightened in the Dragon Ball Z anime adaptation. This is Downplayed since, even in the original manga, Goku experienced a subtle Messiah Creep where he showed more concern for the world, a willingness to sacrifice himself, and worried about people depending on him too much to the point that he boarders on being an Ideal Hero and is treated like a messiah among those who knows him. It's only his Blood Knight tendencies that can override his common sense that makes him remotely closed to being an anti-hero.
Vegeta. In his first appearance, he's the Big Bad, but in the ongoing series, in his effort to beat Goku, he keeps saving the day. He also often unnecessarily endangers the situation by letting his enemies reach their full potential, so he can have a honorable fight.
To a lesser extent, Piccolo could also be seen to possess some Anti-Hero qualities. Though he essentially became one of the good guys after his sacrifice for Gohan, Piccolo was still somewhat aloof, anti-social, and soft-spoken (save for when he launched himself into battle). And though he became one of the Z Fighters, there were still a few instances where Piccolo didn't really view the human members of the team including Yamcha, Chaotzu, and occasionally Krillin (mostly for his cowardly behavior in some situations)as being in his league (though not to the same extent as Vegeta viewed them). He would regularly come into conflict with both of them talking down to each other. The only ones that he generally showed respect to among the big 8 were Goku (Although he gave him one talking to), Gohan, Trunks, and, to a lesser extent Tienshinhan. In The Tree of Might movie, Oolong compared Gohan's new pet dragon to Piccolo, saying neither of them let their guard down around anyone except Gohan.
Yukiteru from Future Diary, after his parents are killed and he takes a level in badass. Later in the series he massacres orphans in the name of becoming God. However, his goal is to bring everyone who died back to life once he becomes god (keeping him from outright villainy).
Likewise, Minene Uryu is one of the craftiest and most resourceful diary owners, and she is not above blowing up a middle school full of kids in order to win the survival game and become God. However, unlike some diary owners, she wants to become god in order to make the world a better place and it's heavily implied that she will revive everyone she kills. Unfortunately for her, in the world of Future Diary, not even God can do that. One has trouble not sympathizing with her when you find out that she's a refugee from an unnamed war-torn country and that she's fighting against serial killers, people that want to become God in order to destroy the world as well as people that want the position just so that they can rule the world.She also works with Yuki to Save the World in the end, too.
Gon is an intensely unlikable protagonist in the original manga. Early escapades include destroying a forest to make a tree mound for himself, and beaching a shark that has swallowed him and feeding it a small piece of banana as it suffocates to death.
The only good guys in Hellsing are anti-heroes or vampire fodder. And then there's Alucard. The only thing that keeps him from being a villain is the fact he is fighting vampire Nazis, although the first anime adaptation definitely plays up the anti-hero side.
Well, Alucard does have his Undying Loyalty to Integra and hates traitors. Plus, he hates vampires that kill needlessly, though not so much because they're killing innocent humans, but more because of the perceived lack of honor involved.
Kikyo was originally a very kind and giving miko. She and Inuyasha had a pact for her to give up her miko duties and for him to become fully human so that they could get married. However, Naraku disguised himself as Inuyasha and killed her. She was later resurrected against her will by dark magic that left her suffering from the hatred and betrayal for Inuyasha that she had felt at the moment of her death. This changed over time from trying to kill Inuyasha to trying to kill them both so they could be together in death then to surviving long enough to destroy Naraku for what he had done to her. Despite her rivalry with Kagome for Inuyasha's affections, she was eventually able to live long enough achieve a redemptive death at peace with herself, Inuyasha and Kagome.
Kagura was created by Naraku out of one of the youkai that had been trapped inside himself for at least 50 years. In return for the hope of freedom in the future, she was forced to work as a slave for him, her life bound because he held her beating heart captive in his position and could therefore destroy at any moment. Despite her position, her growing feelings for Sesshoumaru, coupled with her growing protective instinct for Kohaku all combined to make her increasingly helpful of both Sesshoumaru and Inuyasha's causes. In the end, she was feeding information to both Sesshoumaru and Inuyasha's groups to help them fight Naraku and ended up dying in an Heroic Sacrifice to save Kohaku's life from Mouryoumaru and Naraku's machinations.
Koga, leader of the eastern wolf-demon tribe. Seeking vengeance against Naraku, he becomes a reluctant ally (while maintaining rivalry) to Inuyasha. Thanks to his romantic interest in Kagome, he and his men give up eating human. Koga, Kikyo, Sesshomaru and his followers are described as "Those who, at times will fight, and other times have the same intentions." in Inuyasha Zusetsutaizen Ougikaiden.
Lupin III and his gang go to great lengths to stop evil people from taking over the world, help capture or kill criminals, and even save little kittens. But they're still not heroes. They are usually motivated out of self-interest, and are always criminals.
Nao Yuuki from Mai-HiME is an arguable case; bent on vengeance for her mother, who was severely wounded in a robbery, she uses herself as bait to trap paedophiles, who she proceeds to rob. It's never made clear if her victims receive punishment under a proper judicial system. In fact, she seems to enjoy going after her victims a bit too much.
The eponymous Nadia from Nadia: The Secret of Blue Water is an anti hero. Due to an unhappy childhood and Parental Abandonment, she's grown to be gloomy and depressed, somewhat self-centered and very judgmental. She has an empathic connection to animals and is thus a vegetarian, but can't stand the idea of anyone else eating meat either and constantly berates them for it. Her negative persona is lampshaded in one of the omakes, a character profile, where the narrator just keeps rattling off various flaws ("There has probably never been such a selfish heroine.") and expresses incredulity at how anyone can stand her. However, she is still a fundamentally good, caring person, capable of great self-sacrifice and aware of her flaws. (She even feels bad for occasionally taking her rage out on Jean, to the point where she does something apologetic e.g. begging forgiveness, going on a walk, playing a game of cards, cooking for him, etc.) By the time of the "Where Are They Now?" Epilogue, she seems to have matured into a more sympathetic individual.
Shinji Ikari of Neon Genesis Evangelion is a deeply neurotic protagonist who is withdrawn, socially awkward, and completely lacking in self-confidence, but is shown to be a good person under his many psychological problems, all of which stem from him being the series' resident Butt-Monkey. Asuka, too, fits the role of Anti-Hero, as her only reason for piloting her Evangelion isn't to protect mankind, but to show everyone how talented she is. Somewhat mitigated by the fact that when she was around 4 her mother lost her mind and thought that a doll was Asuka. And her father started to have an affair with the head nurse in charge of Asuka's mother. So at age four, who cares about Asuka? That's right, nobody. So she works around her abandonment issues by trying to get everyone to need her. Because she doesn't want to be alone. Shinji has the same kind of childhood, but works around it by trying not to have to make any decisions, because he thinks he is in the wrong about most things. This show messes up the background history of every character.
Mirielle and Kirika in Noir are assassins, more or less, ruthless, cold-blooded killers. Kirika is saddened, not by killing, but by the fact she isn't saddened by killing, and Mirielle, not even that much, sometimes joking about their kills off-handedly. In this anime, they are the protagonists. There are no traditional heroes in Noir. Except maybe Mirielle's parents.
Who were key figures in the Corsican mob, so their hands weren't exactly clean, either. They set the events of the story (And get themselves killed) by declaring that Even Evil Has Standards.
The Straw Hat Pirates from One Piece. While they almost always do end up saving the day, it's usually because some villain on the island they're on happened to do something to piss them off rather than them acting out of selfless heroism. Luffy himself has made the point that he's not altruistic enough to be considered a hero, and he's clearly more altruistic than many of his crew.
In One-Punch Man, Saitama fights villains simply because he's looking for a Worthy Opponent — that is, someone who won't go down with simply one punch. He chooses to fight villains specifically because of the added bonus of saving the day (which he genuinely enjoys), and he's a pretty decent guy when not fighting.
Another one is Tatsumaki. Although refusing to cooperate with others, she does have the power to back it up. And naturally she acts like a jerk even if she has good goals.
Madoka and Mami are the only characters in Madoka Magica who don't have antiheroic qualities (and Mami gets her creepy moments). Homura is a straight up Anti-Hero, who just wants to protect Madoka at any cost. Kyouko is trying to ignore morality entirely, but is having difficulty doing so and actually reveals to have this behaviour because of her past. She makes her Heroic Sacrifice to protect Madoka and Homura from Sayaka who turned into a witch and generates an explosion. Sayaka wants to be an ally of justice, but is bad at it and eventually goes off the deep end and ends up a witch.
Shinomori Aoshi counts if anyone else does. After he became more of a villain; he started off as an Anti-Villain. Most of the male characters can be: Kenshin himself lapses into this and Sanosuke, who is not afraid to fight against his nation's government. It seems Saitou has an effect on everyone, so it could be said this quality rubbed off nearly as well as anything from Kenshin (Sano in particular).
Ikki Phoenix from Saint Seiya starts out like this. It took some time before he stopped horribly killing every opponent.
The core protagonists of Slayers, which makes the show as intriguing as it is — Lina Inverse is a well-reputed slayer of bandits and has saved the world, but she's only done the latter if the danger she and her companions were in had reached that point. Otherwise, she slays bandits for personal wealth, has no concern for the welfare of innocents (and entire villages for that matter), and will occasionally go to sociopathic levels to get what she wants, even if it includes hurting her friends. Zelgadis is similar to Lina in those aspects, with the exception being that he's more than willing to either murder or flat-out abandon those he cares about entirely.
Princess Amelia is not as much of this as it warrants, but her naiveté on peoples' motives inadvertently make her this — she often relies on stereotypes (such as outward appearances) to determine who is and isn't noble. Gourry the good-natured swordsman would wholly avert this trope if he weren't apathetic to certain worldly events, but that's possibly due to his lack of intelligence. The only protagonist that joins Lina that isn't this trope completely is Sylphiel.
Nicholas D. Wolfwood of Trigun is not amoral by any means, but his harsh "no matter the cost" martialism copied from Knives and Chapel and his sense of fashion screams Anti-Hero, especially when compared with Vash.
Miyu from Vampire Princess Miyu. She banishes the Shinma because it's her fate to do so, not because she cares about the human race. She even uses humans for her personal amusement, just like the Shinma, but arguably not with the same cruelty of the Shinma.
Though after being sold into slavery, Thorfinn eventually develops into a straight up hero.
Yami Yuugi from the early manga. Example: A guy steals a playing card from Yuugi. Yami Yuugi comes out to drive him permanently stark raving mad. Whenever he gets out, someone is gonna die or go nuts. He is smiling as he lights people on fire, condemns them to insanity, etc.
Seto Kaiba in the anime, certainly. First he's a villain. Then Yami Yugi does some freaky shit to his mind and he becomes a sympathetic villain who's just trying to save his brother (and his company), and admits to respecting Yugi. Then he gets kidnapped and Yugi and his friends save him and they team up to beat the bad guys. Then he's a kind of antagonist again but he keeps helping Yugi beat the bad guys. Then they all have to team up to beat more bad guys. Then in the movie he seems to be a bad guy but he's actually a puppet for the Big Bad and helps Yugi to defeat said Big Bad when he's freed from its control. Then he opens a school to help young people learn to duel. Make up your mind, man! He's been on one side since day one. The side where he can screw the most rules.
He's more like an Anti-Hero, the worst kind of hero there is! They give us villains a good name!
First there's the rival, who despite being a Kaiba expy is actually firmly planted on the protagonists side, but uses extremely dubious tactics. He's planning to wage war against a tyrant (who happens to be his father) who uses card games and Child Soldiers to conquer dimensions, and in the process has willingly wiped the memories of his subordinates, recruits child soldiers using war propaganda, lies and manipulates the protagonist in order to better understand his mysterious supernatural powers, apparently experiments on children ( although that one he only talks about doing so to Sora, and appears to genuinely care about Reira), lies and manipulates everybody, and spies on everyone. He's mostly A Lighter Shade of Grey because a) he didn't start the war, he's just trying to end it, and b) unlike his father he's never tried to commit genocide.
Then there's Shun. A survivor of the aforementioned genocide, all he wants to do is rescue his captured sister and comrades. Like Reiji, he has very few limits when striving for this goal. He's killed not only enemy soldiers but also innocent people when he thought it might help him capture an extremely valuable hostage, once tried beating an enemy to death, and he's a general Jerkass loner.
The core four in Yu Yu Hakusho, all to varying degrees — Kuwabara being the least so, Hiei being the most.
A classic example is Raven in Zoids: Chaotic Century Once you get to the last episode, he's screaming anti hero.