Light Yagami, the Villain Protagonist of Death Note. Death is the only punishment he can dish out. Early on, he states that he's going to create a world filled with only good-hearted people he approves of. He's simply going to start with the criminals... but it's quickly subverted, when in the second chapter he leaps off the slippery slope and begins to threaten and kill all those who oppose Kira, including the police officers.
Lelouch in Code Geass, in creating the terrorist group the Black Knights, is trying to overthrow Brittania's racist, Social Darwinist regime, so as to create his sister Nunnally's longed-for "beautiful world."
In Romeo X Juliet, Juliet starts out disguising herself as one of these, nicknamed "The Red Tornado".
Tista from the Tista manga would probably constitute as a female example of this. She is an assassin who kills immoral people who the law cannot catch.
Hibari Kyouya from Katekyo Hitman Reborn!. He rules Nanimori with an iron fist and does whatever he pleases since people are too afraid to call him out on it, but god help you if you so much as look at his hometown the wrong way.
Triage X follows an entire team of medically-themed vigilantes who kill gang leaders, mob bosses, and other menaces to society.
Lunatic in Tiger & Bunny. As opposed to Heroes who take part in HeroTV who only seek to arrest criminals, Lunatic actually kills them. Though he tends to save this for people who REALLY deserve it.
Jellal becomes this in Fairy Tail, forming a small independent guild that hunts down dark guilds, something the Council doesn't allow of the guilds in it's jurisdiction, as it counts as illegal warring between guilds.
In Future Diary, the Twelfth is a vigilante whose heart seems to be in the right place: his goal is usually just to capture criminals to help the police, not kill them outright. However, he dresses and acts so creepily that the people he's trying to help often beat him up or arrest him. Then he gets involved in the Diary Game and starts killing with no remorse, since he feels that "Justice" is on his side.
V from V for Vendetta. While throughout the series he's seen as more of a... vengeful terrorist, he does show some (although few) signs that he started out as one of these and simply got tired of not making progress.
Rorschach is a deconstruction of this trope, as well as the Anti-Hero in general. He is not presented as a good person and the police disdain him — in fact, they hate him almost as much as the criminals do.
Truth in advertising: DC Comics' Adrian Chase—a district attorney, and later judge, who hunted down and killed crooks who got off—was named simply The Vigilante.
Though Chase eventually became a Deconstruction of vigilante justice, and ended up committing suicide due to his guilt over the increasing violence of his methods and actions.
Also from DC and similar to the above example is federal prosecutor Kate Spencer, who became the vigilante assassin Manhunter after she got tired of criminals dodging legal justice.
The Crimson Avenger, who also has the honor of being (disputably) The DCU's first masked superhero.
The Huntress in DC Comics became a vigilante after her family was murdered by rival mafiosi.
Jason Todd became one of these after coming Back from the Dead, criticizing Batman for being too "soft" on criminals and wanting more than anything to kill The Joker.
The Paladin, who appeared in a Justice League of America story where Anansi was changing all the hero's stories, is an alternate Bruce Wayne who picked up Joe Chill's gun while he was running off, and shot him. He became a gun-toting vigilante in a cowboy hat, whose story (until Vixen interferes) ends with him and Commissioner Gordon in a Mexican Standoff.
Wild Dog in DC Comics is a largely unknown vigilante. He's basically per his creator Max Allan Collins in Amazing Heroes#119, a modern version of the Shadow, Zorro, the Lone Ranger, and the Green Hornet.
John Dusk, the protagonist of Absolution. He's a superhero in a setting where the superheroes are all legitimate law enforcement officers, which means they have to observe due process and other pesky legal restrictions. One day, he gets fed up with having his hands tied, and starts killing.
Eric Draven in The Crow. (Although, since he's already died and has resurrected as an unkillable zombie, he's technically a Vigilante Thing.)
In The Question, the Mikado was a physician who started inflicting Karmic Justice on those who caused the pain he saw every day in the ER. A man who scalded his newborn baby was boiled alive, for example.
Find a hero who doesn't fit this trope in Sin City.
John Tensen from The New Universe title Justice. In early issues, when he thinks he's a warrior from a Magical Land, he goes after criminals in general. After a Retcon reveals that he's actually a paranormal, he devotes himself to policing his brethren, punishing the ones who use their powers for evil.
Victor Ray from 100 Bullets kills criminals in his spare time to balance out the awful things he does on behalf of Agent Graves
Depending on the story, Paperinik (Donald Duck's superhero alter ego in some Italian stories) may have this as his reason to hunt down criminals: Duckburg has a serious criminality problem (seriously, how is that the Beagle Boys manage to get free in a lawful way?!), and an unstoppable sadistic superhero going to extreme lengths to humiliate and beat you up after catching you in the act or getting proof and a confession (justifying the fact his victims are always guilty: he makes sure, and those times he was wrong he found out before beating up the supposed criminal) tend to keep the problem manageable. In those stories he's also a wanted criminal due various spectacular thefts he committed at the start of his career to punish Donald's bullies (the very first being the money-filled bed Scrooge was sleeping on: the sacks of money were too easy for him), but most of the police doesn't want to arrest him due a combination him catching an insane amount of criminals and leaving them on their step and mercilessly humiliating the ones who actually try and arrest him (one memorable occasion had him fooling two cops into breaking into the bedroom of the chief of the police. Hilarity Ensued).
In the movie Punisher: War Zone, the "victims are always guilty" rule was notably averted: near the beginning of the movie, he discovers that one of the people he killed was actually an undercover FBI agent with a family. He feels so guilty about it that he offers said agents widow a bag full of mafia money, as well as the chance to shoot him.
The Death Wish movies. Paul Kersey becomes a vigilante after his wife is murdered and his daughter is sexually assaulted by muggers. Also an Unbuilt Trope as the film pioneered the urban vigilante concept, but it also showed how dangerous it would be.
By the time of the third sequel, Kersey is infamous for harrying the police, who are powerless to pin any charges on him (but are happy to take credit for his crime-fighting accomplishments). Police Chief Richard Shirker tries to contain him, but ends up joining the fray when Kersey is ambushed by gangsters.
Kersey:You stuck your neck out for me? Shirker:(dying) It was you or them.
This movie actually explains the difference between Cowboy Cop (Harry) and Vigilante Man (vigilante policemen). Dirty Harry uses excessive force when fighting criminals who forcefully resist arrest or directly endanger innocents (his iconic do I feel lucky? speech actually taunts the criminals to give him reason to use lethal force). He doesn't hunt and kill unsuspecting criminals (when Scorpio is released on a technicality Harry tries to scare him, when Ricca is acquitted on legal loophole, vigilante cops immediately kill him, his lawyer and even his driver).
The movie The Star Chamber is about a judge who decides to join a group of judges who are disgusted with the system and become vigilante men. But during one tangled affair involving drugs, the protagonist comes to realise that justice means something more than arbitrarily killing criminals.
Jodie Foster in The Brave One plays a female vigilante, in a meditation on the paranoia and isolation the life of the Vigilante Man(or Woman) would entail, especially if they used to be a "normal" person. Interesting callback to the first Death Wish in her chosen method too.
Inverted in the Western movie Hang 'Em High. Clint Eastwood is the innocent victim of vigilantes who mistake him for a murderer/cattle thief (he unknowingly bought the cattle off the real killer). He then becomes a deputy to bring them to justice, and must resist pressure both situational and personal to take the law into his own hands.
Contract on Cherry Street (1977) has Frank Sinatra as the leader of a team of NYPD detectives who turn vigilante on The Mafia after one of them is killed.
Savage Streets (1984) has Linda Blair as a tough high school girl who turns vigilante after a vicious gang called the Scars rape her deaf-mute sister and murder her best friend.
Two Fathers' Justice (1985). A newly married couple are killed by drug dealers, and their fathers (reluctantly) team up to track down their killers who've fled the country.
In Pyrokinesis, the protagonist is a rare female example, killing criminals with the titular psychic power. She manages to stay a good guy despite fighting against the police, because the chief of police is also the head of the snuff ring she's been targeting.
In TMNT, Raphael becomes the Nightwatcher while Leonardo is in South America. TMNT being a kids' movie, Raph doesn't kill anybody, but he doles out some major beatings to all criminals he comes across.
The Sally Field movie Eye For An Eye has Field's character lose her daughter to a serial killer, and stumble onto a conspiracy of Vigilante Men at a support group. They have very specific requirements: They only target killers whose guilt is obvious yet get Off on a Technicality, and they won't make the kill themselves. Instead, they teach newcomers how to make the hit themselves. Something of a strawman case; the FBI has recognized a pattern of suspicious deaths among acquitted killers and has planted spies in support groups to protect those killers. Fields discovers the spy in time to keep from incriminating herself seriously, but the agent still threatens Fields with life in prison. Despite being fully aware that the killer has killed again. Ultimately, the FBI is powerless to protect the killer, as Field pulls off the conspiracy's plan perfectly - make herself the killer's next target, then kill him in self-defense.
Hard Candy: Hayley may qualify as one due to her crusade against pedophile rapists. That or she may be a budding Serial Killer.
Joey Rosso from Rolling Vengeance. His weapon of choice happens to be a Monster Truck!
Deconstructed with Keller Dover in Prisoners, who nails the wrong man for kidnapping his daughter, crosses the Moral Event Horizon as a result, and is left to die in a pit by the real kidnapper for his trouble. The ending leaves it ambiguous whether or not he will be rescued.
Mack Bolan, the protagonist of The Executioner series of novels, started out as this. The series eventually had him join the government, in a black ops organization. He did have a moral dilemma breakdown during one mission in China however, when he was forced to strangle a 14 year old girl to death because she was a gun-toting fanatic. From that novel onwards he's one of the more restrained members of the Stony Man Farm.
The Veteran: James Vansittart deliberately makes sure the killers are released so rogue members of the Metropolitan Police Service can strangle them to death. , 
The nameless cabal in Already Dead doesn't kill their targets themselves. Instead (for a hefty fee), they offer to hunt down the person who committed the crime and turn him over to the victim — complete with a very large table full of things like drills, knives, hammers, and blowtorches.
Kyle Youngblood in the Dr. Death series of novels winds up living up to his name to his friends and family as well as his enemies, as their retribution drags them into the crossfire often. The only friend he has who never dies is Rafe, the one who accompanies him personally on missions. Everyone else? They're gonna get snapped, gunned down, or exploded sooner or later. Interestingly, he prefers to use traps whenever possible as opposed to charging in guns blazing. The mercenary known only as "Big Cherry" due to his eye having been gouged out, and he refusing treatment or a covering due to the badass points it gives him, plays the trope straighter despite being a designated antagonist. He'll take out those he finds unpalatable on the way to his intended targets. Think Mad Dog, from the Time Crisis games, sans megalomania. (as well as always wanting a fair fight with his rival for example) Kyle usually kills his bosses, causing Cherry to once more swear revenge.
The Saint is a Gentleman Adventurer version who does his vigilante thing not because of any specific need for vengeance, but because he enjoys the challenge of defeating people who believe they are untouchable In the earlier novels, he was much more likely to kill the villain of the piece; later stories saw this toned down, and by the time the stories were no longer being written solely by Leslie Charteris, it had virtually vanished. Every so often he would remember his 'bad old days' and choose to extract fatal vengeance someone the law could't touch.
The Spider, The Shadow, and numerous literary adventurers of the pre-World War II era fit this trope. In fact, these personages adopted secret identities due to the fact that they knew that they police would arrest them for their sudden justice. Other than Doc Savage (who didn't kill his opponents except when it was completely unavoidable — he just shipped them off to be lobotomized or the equivalent) and the 1939 introduced The Avenger, relatively few of the serial magazine protagonists of this era worked with the open approval and admiration of the police.
The Bluejay, also known as Mortimer Folchart in The Inkworld Trilogy shows shades of this, particularly in the third book.
Vigilante man? Try vigilante GENERAL!!! Ben Raines of the Ashes series by William Johnstone. Imagine if the Punisher saved America by being the post-apocalyptic George Washington. Imagine the rest of the world is made of alternately criminal drug-running dictators or tree-hugging communist hippies. And now imagine he's just been elected president. And you still only have a TENTH of the insanity of this world. Raines does such downright crazy and morally black shit sometimes that not even [[Tabletop Game/Warhammer40000 The Emperor]] would approve of (like blitzing a city of war orphans being brainwashed into child soldiers just so it won't cost him a single Red-White-And-Blue-Blooded American life, or monologuing about how children who grow up in slums can never know what the good life is to reporters, then gunning them down on live television), and that's a crapsack UNIVERSE. Essentially, he commits vast atrocities on par or above standard Crapsack World characters, both heroes and villains, simply because he is as risk-averse as a cuddly soccer mom. A cuddly soccer mom with nuclear arms, miles of artillery shells, and a fetish for napalm and fuel bombs. Small wonder anybody with any semblance of religious leaning considers him the Antichrist. (A lot of it scarily justified through 'sins of the father/brother/sister/mother' arguments, then again the author's father was a fire and brimstone kind of minister.)
In Ian McEwan's novella Black Dogs, the narrator becomes a Good Vigilante Man after he sees a man in a restaurant smack his kid across the face so hard the kid's chair is knocked over backwards and cracks on the floor. The narrator challenges the man to "fight someone his own size" and then manages to break the guy's nose and knock him out with a few punches. He is called off by a waitress and stops him just before he becomes He Who Fights Monsters and kicks the guy to death. This moment provides a contrast from the Grey and Gray Morality of the rest of the book.
Nuklear Age presents The Civil Defender, a crazed vigilante hell-bent on eliminating all crime, no matter how small. Complete with machine gun and futuristic body armor, the Civil Defender took up being a vigilante when his sandwich was stolen, and gives out tickets written on notebook paper when he's sane enough to have his finger off the trigger of his machine gun. He has repeatedly given out tickets for littering because of the pile of other tickets he personally threw to the ground.
Sisterhood Series by Fern Michaels: This series is about Vigilante Women! They obey a Thou Shalt Not Kill code, give villains a Fate Worse than Death, and they are usually careful to Never Hurt an Innocent. The book Free Fall had them being arrested by the police, but that's okay, because the judge, prosecuting attorney, and defense attorney are secretly on their side, as well as being considered heroes by a lot of people! Later on, you have a group of Vigilante Men made up of Jack Emery, Harry Wong, Bert Navarro, Ted Robinson, and Joe Espinosa!
The Dresden Files: Harry Dresden has always been more or less willing to blast his way out of trouble (for which he's earned a reputation in the magical community as a thug), Karrin Murphy not so much. She believes in the power of the law, and her gradual acceptance that this trope is ever okay is a large fraction of the Darker and Edgier path the series has taken.
Live Action TV
Buffy the Vampire Slayer: Willow Rosenberg kills Warren (whom everyone figures deserves it) and tries to kill Andrew and Jonathan, even though they're only guilty by association.
Dexter Morgan from Dexter sometimes sees himself as a vigilante for killing murderers, and in one episode fantasizes about being a superhero who is applauded by the public and in another, has a brief daydream where he acts as a Batman style vigilante Super Hero but quickly dismisses it as ridiculous. In his darker moments, however, he admits that he's just a monster with a little more self-control.
The TV series The Shield is about a cop who is a Vigilante Man. Interestingly, the series constantly shows that Mackey's vigilantism is a bad thing, always for his own self-interest, and never in the interests of justice. Then, it goes on to show his Cowboy Cop side, where he bends or outright breaks the law to serve the greater good (a criminal will go free, but the young girl he kidnapped will be saved from being raped and murdered). Notably, the series never specifically casts judgment on Mackey's karma directly, leaving it to the viewer to decide whether he has overall good karma or bad.
Desconstructed in an episode of Michael Chiklis' previous series, The Commish. The episode features a vigilante who tapes his acts and sends them to the press. At first, his actions are relatively innocuous (running criminals off the road, then humiliating them), and even the cops are cheering him on. Commissioner Tony, however, thinks the guy is bad news. He's proven correct later when the police arrest a man for a brutal rape/murder, then release him after realizing he's innocent. The vigilante, wrongly believing the innocent man got Off on a Technicality, goes to the guy's home and clubs him to death. The vigilante then becomes the cops' target for the rest of the episode.
Disgruntled cop Manny Lopez in the MacGyver episode "Tough Boys" decided to use his Marine skills to train a bunch of kids to become the titular Tough Boys and crack down on drug dealers after snapping from the trauma of having a crack addicted daughter that went missing without a trace leaving him with his drug-addled baby granddaughter. Predictably, the episode ends with Mac having to save the Tough Boys from being nearly killed in a shoot-out and preventing Lopez from blowing himself up along with a major drug dealer.
The Equalizer clearly draws on the vigilante justice issues raised by Deathwish and the Goetz trial (as seen in the Mad Magazine spoof of this TV series, where Robert McCall, Charles Bronson and Bernard Goetz argue over who should shoot a subway mugger). McCall never actually shoots anyone in cold blood however, preferring to use psychological warfare to inspire a confession (though quite a few villains conveniently pull a gun at the end so McCall can shoot them in self-defense).
Millennium. The Judge is a pig farmer who uses ex-convicts to inflict Karmic Death on people he believes have escaped justice, such as a landlord whose negligence caused the death of an elderly tenant and a detective whose false testimony sent an innocent man to prison. He invites Frank Black to join his cause, but when he refuses the Judge hits the police with a lawsuit to make them back off. Unfortunately for the Judge his ex-convict killer regards this as hypocrisy, hamstrings the Judge and throws him to his own pigs to be eaten alive.
Dark Justice, about a judge who delivers Karmic Retribution to criminals who get off on technicalities, with the aid of various helpers, usually low-level criminals working off their 'community service' sentences.
The protagonist of the ITV series The Fixer killed his aunt and uncle for molesting his sister. This apparently qualified him to work as a covert government hitman. In one episode he's ordered to kill his predecessor, who has turned Rogue Agent and started killing drug dealers and prostitutes.
In Justified, Boyd Crowder seems very much this after he apparently gets religion, but the series leaves it ambiguous as to whether he really is or is just faking it an attempt to erect his own criminal empire. Unlike most vigilante men, he doesn't seem to prefer lethal force, and at one point kills someone innocent even by his Well-Intentioned Extremist standards. Rayland harries him the entire season, but when the chips come down, he is revealed to actually be a vigilante man after all, and at the end of the season he goes off apparently to basically become Batman.
The ones from "A Real Rain" and "Reckoner" were fairly standard, killing people who'd been acquitted of crimes or who got lesser sentences (though the one from the latter was actually a Professional Killer paid to act as a vigilante)
The one from "True Night" killed off members of a brutal street gang, but was psychotic and didn't even know what he was doing. The BAU mentioned that because he was so severely ill, it was only a matter of time before he became a danger to ordinary people as well.
The priest from "Demonology" could also count, since he was killing the men believed to be responsible for the death of a fellow priest, and close friend of his.
In Flashpoint, there was an episode of a man going after drug dealers and ultimately the main drug lords because his brother had been killed from a drug overdose given to him by these people.
In Bones, Broadsky the rogue sniper fancied himself a vigilante but is really just a madman who will kill anyone who gets in way and feels no guilt for killing innocent bystanders.
Russian 2009 series Меч (The Sword) presents a group of vigilantes hunting both criminals and corrupt officials who help criminals evade justice. Interestingly, the group consists predominantly of former or active civil servants (ex-detective who resigned after being proposed a bribe by his own superior, ex-cop sentenced for murder of a rapist, young traffic police officer, retired FSB agent and state prosecutor).
Arrow - 'The vigilante' is even one of Oliver's titles in the show...
The Castle episode Heroes and Villains features a vigilante that actually dresses like a superhero. While he initially used nonlethal tactics he eventually commits a murder. It turns out that the vigilante, a female police officer by day, was innocent of the murder. The real killer impersonated her.
The Abney Park song "Victorian Vigilante" is about one of these.
Woody Guthrie's "Vigilante Man" is actually about how American workers would be attacked and beaten by the people of the towns they passed through during The Depression.
The New World of Darkness sourcebook Slasher, which is all about serial killers who rise above the cut, has an entire Undertaking dedicated to this — the Avenger. They get the ability to take on multiple foes at once without being overwhelmed, but have to actively make the effort to break from their pursuit.
Dark Champions contains rules for several modern-day action genres, but defaults to vigilantes taking down criminals. This shouldn't be surprising, as the original 4th edition book was inspired by Steve Long's personal PC the Harbinger of Justice, who is this trope cranked to max.
Oasis from Sluggy Freelance took on this role when she lived in Podunkton, killing pretty much the entire mafia establishment in town, as well as any miscellaneous crooks who pass through. She seems to do this largely out of boredom. However, since she had previously been an Ax-Crazy assassin who'd kill anyone who came between her and Torg, this vigilante justice is actually a sign of Oasis becoming less violent.
She also used to partner up with Vriska in FLARP session to kill off other players, but only the ones that really deserved to be punished. She leaves when Vriska starts murdering indiscriminately.
Axe Cop. The police are after him, everyone he kills is evil, and he uses lethal force against pretty much everyone "bad". Though he switches back and forth on the killing of public servants (he beheads many FBI agents to protect Uni-Baby, but is unwilling to kill the police officers trying to arrest him).
Less Than Three Comics' Shadow attacks crooks in the street, and uses fear to scare them straight. It's worked pretty well so far.
Yuri Lowell of Tales of Vesperia. He grew up in the slums of The Empire which rules most of the world with his friend Flynn Scifo and joined the Imperial Knights with him. After growing disgusted with the government's weakness and the cruelty of the nobles, he left Flynn to try and reform the Empire from within while he seeks to give the commoners the justice that the current system denies them. Later on, he joins up with the Guild Union in the hope of eliminating injustice from the world completely. He is rather Genre Savvy; knowing that his actions are unlawful and may bring him closer to what he hates, he is willing to break the law anyway if it serves the greater good.
There is also a sidequest involving a Vigilante Man who has less scruples than Yuri.
Mass Effect 2 has Archangel, who turns out to be a Cowboy Cop frustrated by being hindered by ineffectual bureaucracy. Nicknamed "Space Batman" by the players, though he's much closer to Space Punisher as he has no problem killing criminals. He's so good at it that three rival mercenary groups that hate each other's guts team up to take him down. He also isn't above cruel punishments, like killing criminals by sabotaging the air supply of their space suits or infecting them with their own bioweapons.
The Yatagarasu in Ace Attorney Investigations, a noble thief who steals information on corrupt business dealings and sends them to the media. Establishing the identity and motivations of the Yatagarasu and its target are a big part of the game's plot. Kay Faraday tries to pick up the tradition after the first Yatagarasu is put out of action. She's not very good at it.
The title character in the aptly named Vigilante is officially this, although the focus is more on the quest to rescue his girlfriend.
The title character of Anaksha Female Assassin is a vigilante assassin who has taken it upon herself to clean up the streets of Santa Lina, one scumbag at a time.
To a degree, Yun and Yang from the Street Fighter series, as the twins strive to protect their beloved Hong Kong from all kinds of peril and use their martial arts to do so. Specially emphatized in Street Fighter Alpha III, where Yun chases after Fei-Long when he and Yang take rumors about him being in the drug trade at face value. The real culprit is Vega/Bison.
The titular character of Max Payne. His motivation is real Punisher-like as well (his family is murdered and he'll throw everything he's got at the people who did it to make sure they pay).
According to supplementary material for 3, the Cracha Preto were originally lawmen hunting down criminals the law couldn't or wouldn't touch. Originally.
The protagonists of Final Fight are out to stop a criminal organization that took over the city and kidnapped the mayor's daughter. Said protagonists include a ninja, the mayor's daughter's boyfriend, and the mayor, himself! (Helps that said mayor is a former wrestler.)
The three protagonists of the original Streets of Rage were police officers, but when The Syndicate took over the city, including the police, the three officers quit in order to take on Mr. X and company themselves.
Bernie Goetz was labeled the "Subway Vigilante" after he gunned down four men who werenote probably, there was some disputemugging him. The incident sparked a national debate on vigilantism, though his actions do not fit into the classic mold of a vigilante.
Three-time killer William Inmon was a self-proclaimed vigilante. His arguments for this are unconvincing.
The term comes from the Vigilance Committees set up in the old west when settlement had outrun the law. The actual behavior of these was more complicated then the tradititional Torches and Pitchforks one, though that picture is hardly without merit. Some lawmen, for instance, found it useful to use these as material when forming posses.
The Whitechapel Vigilance Committee tried to be this in the days of Jack the Ripper. Tired of the police not catching the criminal, they sent out men on patrols round Whitechapel and tried to investigate the case themselves. Which didn't do a lot, the Ripper himself was confident enough he wouldn't get caught he sent the letter with half a human kidney attached to their leader.
In Italy it was so diffused that Italian language has the word giustiziere specifically to denote this. The fact it's derived from the Italian word for "justice" should be enough to explain why it was so diffused, and why the mindset is still there.