Amano Jaku from the manga version of Urotsukidoji is an unsympathetic, selfish, and sociopathic jerkass who only cares about getting laid and doesn't give a rat's ass about the people around him. The only "heroic" thing he actually does is saving a baby from being ran over by a truck, though this is only before he heartlessly tosses the baby into the river calling it a waste of time and saying that he hates babies and old people. Thankfully his anime counterpart is much more heroic with a majority of his nasty traits from the manga being left out completely.
Buju from Urotsukidoji III manages to be even worse than Amano's manga counterpart. He is a vile, nasty, perverted and unlikable psychopath who has no qualms about murdering families (including babies) and raping women and likes getting drunk in his spare time. Even after his supposed "redemption", he's still pretty much the same as he was in the beginning. For example in Urotsukidoji IV, instead of saving a female character from being raped by a demon, he chooses to watch instead as he says he enjoys seeing women getting raped. The only thing that prevents him from being a Complete Monster is his love and protection for his adoptive daughter, Himi. Though it still doesn't make up for his despicable personality.
Dominion Tank Police: There really is little quantitative difference between the cops and the crooks. Both prefer to drive large, destructive vehicles, and both cause massive amounts of collateral damage to life and property; one side merely has the advantage of legal sanction for their acts, while the other's motives are purely mercenary. This is most clearly lampshaded in the sequel series, wherein Anna and Uni are allowed to make a Heel–Face Turn without the least change to their personalities; they've reformed because they're tired of being chased by the police and have realized that being cops would allow them to continue blowing stuff up, but also provide a steady source of income.
In the first Dominion Tank Police, there is an exchange between squad leader Brenten and Lovelock that illustrates this mentality perfectly. Brenten, probably the next most gung-ho member of the squad besides Leona, and most definitely a dyed in the wool veteran of the squad, suggests to Lovelock that they should quit the force right then, and go off and become criminals, for the action, the money, and the lack of regulations that plague them as Tank Police. From the tone of voice, it's clear that he's saying this in a half joking, half not manner, suggesting that if Lovelock had agreed to this, they would have actually left for a life of crime right then. When Lovelock declines, Brenten immediately recants everything he said, and nothing more is ever said of it again. Dominion is not a serious series, and the fact that the so-called "heroes" are just as bad as the "bad guys" (and sometimes worse) is part of the joke.
The title character from Nadia: The Secret of Blue Water also qualifies. She's moody, distrustful, bad-tempered, and suspicious about everything. But she's also a Not Good with People sort of person who has never socialized with anyone before except animals. As such, she is unable to recognize how she feels about anyone. As a result of Jean's love, however, she is gradually transformed by the end of the show and uses the Blue Water's power to resurrect the latter when he is killed by Gargoyle.
Fushigi Yuugi's Mayo Sakaki. A Clingy Jealous Girl inflicted with some of the most severe Moral Myopia ever, and walking factory of Kick the Dog and Shoot the Dog moments. Becomes a Karma Houdini because the writer expects us to sympathize with her, despite everything she pulls, and is even thanked by the people she spent all of Eikouden mind controlling or trying to kill. She'd be a Villain Protagonist except that the author insists she's just an ordinary, lovesick girl who didn't understand the circumstances she was in.
Mobile Suit Gundam 00 gives us Celestial Being who, in the first season, were essentially unusually well-armed private army who tried to beat the rest of the world into submission on the orders from an Omniscient Council of Vagueness (which was later quietly forgotten). They only targeted military facilities and units, however, and were intentionally shown as Nominal Heroes who were often fighting for their own deep-seated issues, in an organization whose master plan was to unite the world by becoming the focus of their hatred. In the second season, authors turned the Big Bad into a Stupid EvilCard-Carrying Villain and portrayed Celestial Being as noble heroes. Although Character Development (and in one case, replacement) was in plan, many fans were unsatisfied with the shift to near-Black and White Morality.
Kio Asuno of Mobile Suit Gundam AGE is a rare instance of this trope with a nice character. He was initially sympathetic, being a Child Soldier raised by his vengeful grandpa to see Vagan as inhuman monsters before meeting with them and sympathizing. When Kio decided to stop killing, however, he also stopped even defending himself in battle. His wingmates told him repeatedly this put them in danger as well as himself, and every enemy he spoke to told him to shut up, but Kio ignored this and continued doing the same exact thing every battle. He also bartered away the Gundam's secrets to the Big Bad, which destroyed his side's major advantage. Nevertheless, the show sided completely with his point-of-view as though there was no middle ground between genocide and Suicidal Pacifism.
Gokudo plays with this. From the beginning, the title character is an unlikable ass who uses anything thrown his way to cheat and steal, but everyone always tells him he's the hero of the land. After the first few episodes, he's tricked into killing the Big Bad. Eventually, he uses his Genie to stop being the Designated Hero and sends the world back In Harm's Way because he finds the happy evilless world exceptionally boring.
The protagonists from Dragon Pink. The only good character is a put-upon Cat GirlSex Slave. In one scene they encounter a group of "Slave Knights", skeleton warriors who defend themselves by keeping a naked girl hostage in their torso as a human shield. The protagonists say "Sorry!" and slash right through one of them, including the hostage. It really says something when the monster is shocked by their callous behavior.
The whole cast really mainly because this show runs on Comedic Sociopathy. Whether its the Yandere Shoko or the Brocon Akira, practically every sympathetic character has serious personality flaws to the point where they qualify under this trope.
Vulcan, the main character of Lets Bible, who, within 5 pages of his introduction, knocks the female lead unconscious and drags her onto his boat with the intent to rape her. When the two of them get attacked, the only reason he protects her is so that he can have his way with her later. Only sheer amounts of Crazy Awesome and Rule of Funny stop him from being completely unlikable (and the fact that he gets better eventually.)
Kaname from Vampire Knight is presented as an antagonistic character throughout the entire story, but it hits full force when he disappears about halfway through without giving a reason and starts murdering and manipulating other vampires who are in turn presented as victims. Towards the ending however, it's suddenly revealed that he didn't really kill his first victim, which somehow, makes him innocent and heroic for having "merely wanted to push people away", and everything else he did is more or less forgotten about - including having murdered the family of one of the other protagonists.
As noted by Bamboo Dong (on both of her articles on The Stream, and Shelf Life), Akatsuki of Aesthetica of a Rogue Hero is this, to the point where she felt uncomfortable watching it, and on its original stream, dropped it after 4 episodes. Akatsuki constantly forces women to wear demeaning clothing, disrobes them, humiliates them, like forcing them to wet themselves, and constantly gropes them, all while the show attempts to justify it, and tries to show why he should be rewarded for it. (“He means no harm!”, “It’s not rape because she’s asleep!” etc.)
This is one of the reasons why Chargeman Ken has become a meme. Ken acts like a jerk most of the time. He kills people without caring if they are human or the enemy aliens. He once killed an innocent professor by using him as a torpedo.
Re:CREATORS is a series about fictional characters coming to life in the real world; as such, they undergo significant Character Development. An in-universe example would be Aliceteria February. In her homeworld, she is supposed to be a brave and heroic knight, but ends up opposing the other heroic characters and puts innocent people in danger if it means saving her world. After her friend Mamika gets killed, she ends up flying off the rails and attempts to kill Meteora based on circumstantial evidence and even when Sota attempts to appeal to her better nature, she refuses to listen to him and even attempts to kill him if it means getting her hands on Meteora.