Catwoman has been this for decades, though she has settled on "antihero" since the 90's.
Magneto of X-Men. Takes wider swings across the spectrum than any character in comics.
Mystique, with an actual revolving door reference here. She's been a Card-Carrying Villain, federal agent, terrorist, spy and full-fledged X-Man at various times, and that's not even getting into her Expansion Pack Past.
Deadpool wavers between mercenary, good guy, or doing merc work for the bad guy of the week. This is due in large part to the fact that he's insane.
It's a fairly well documented fact that any time a villain becomes popular enough, Marvel will take a stab at making them a hero, or at least an anti-hero.
Arguably the most ridiculous example: their repeated (at least three times) attempts to make sociopathic casual killer and rapist Sabretooth into an X-Man. At least they recently seem to have realized that rehabilitating him will never pan out, and resorted to coercing him into behaving himself. Although there have been at least two alternate universe versions that exist primarily to allow a heroic Sabretooth without all the baggage.
And now there's a flashback storyline running, from a period when Sabretooth was somewhat less insane (presumably, the processes that Weapon X had used to control him when he was an assassin hadn't completely worn off yet) and not yet in a blood feud with Wolverine, in which he's a Punch Clock Hero. He doesn't much care about helping young mutants, but as long as the checks keep clearing...
Wolverine of all people could be considered this. Although he'll never outright betray the X-Men and is always there for them if they really really need him, he'll also constantly run off for his own personal reasons at the drop of the hat. Despite being warned often that he can't come and go as he pleases if he wants to be a full member of the team, he always does, and the X-Men always take him back.
Magneto's children Quicksilver and the Scarlet Witch started as members of the Brotherhood of Evil Mutants then reformed and joined The Avengers and have been ping-ponging back and forth between heroism and villainy ever since. Quicksilver primarily because he'd really like to be a hero but is too self-centered to not do something he thinks will improve his situation just because it's illegal or wrong or something; Scarlet Witch primarily because she has a mental breakdown whenever a writer can't think of something more interesting to do with her near-omnipotent powers.
When Harley had her own series, the writers worked around this by generally reserving her homicidal tendencies for other villains. Good guys and innocent victims usually ended up knocked out or Bound and Gagged at worst.
Poison Ivy, while always a villain when on her own, tends to reform (or at least become neutral) whenever Harley is attempting to reform.
She was even a member of the Birds of Prey. Though that was entirely for selfish reasons, and she betrayed her teammates once she no longer got anything out of the deal.
In his very first appearance, Two-Face had captured Batman and was throwing the coin for whether to kill or free him. Batman asked what if the coin stood on its edge? and got Two-Face to agree to surrender and submit to plastic surgery and therapy. The coin — substituted by Batman for the real coin — stood on its edge, and Two-Face returned to a normal life. However, he was later injured again and return to his life as Two-Face.
In No Man's Land an act of ungodly luck makes Two-Face a good guy for what looks like weeks if not months. He agrees to help Renee Montoya to try and take care of the weaker people in the city; injured, old, children, etc. Each time he helps he flips a coin, according to Montoya he apparently flips the "good" side over 100 times......in a row. It's possible that the implication there was that Two-Face was cheating. Perhaps he had honestly (temporarily) reformed, but pretended it was all the coin's fault (so he'd have an excuse if he ever turned evil again). And if that's not it, maybe Batman or Montoya just slipped him a weighted coin.
Batman villain The Riddler sometimes went through the door as well, though currently he's a Face. It's unknown whether he will become a Heel again.
Spider-Man "villain" Venom had a tendency to hop back and forth between villain and anti-hero (usually dependent on whose perspective a given book was shown from). Sometime in the '90s it just became accepted that he was an anti-hero, never really being cast as a proper villain, even when working as an enemy to Spider-Man. This is likely because his villain gig was taken over by his "son", Carnage. Then there was a period where the Venom symbiote was bonded to the Scorpion (definitely a villain) and the original Venom was Anti-Venom. Then it got bonded to Flash Thompson, who did his best to stay on the anti-hero side.
The character "Toxin" was created to fit the other end of the Venom scale. Toxin is the symbiote child of Carnage who bonded onto a law-abiding police officer. While the struggle with the Symbiote's natural killing desire is intense, Toxin is a more straight example of a heroic Venom.
Same with Morbius who started as an anti-villain, then went to being the anti-hero of his own series, eventually got upgraded to a Nineties Anti-Hero who constantly fought against Spiderman yet would help people in need, unless he felt like eating them.
Namor the Sub-Mariner deals with this so often that the trope may as well be named The Namor. He fought the original Human Torch (that's bad) and allied with him against the Axis in World War II (that's good) then swore revenge against humanity when he thought they'd destroyed Atlantis (that's bad) then swore to defend Atlantis once it was discovered again (that's good), and the frogurt is also cursed (that's bad). To put it another way: Marvel currently has two "ruling councils" of good guys and bad guys. Namor is on both of them.
To expand on some of Namor's more recent history: Turns out he had sleeper-agents in America (bad), but then he helps Captain America's side in the Civil War and promises to have all sleeper agents removed (good), he lied about the sleeper agents (bad), successfully stops his son Kamar from an attempted coup and starting a war with America (good), unfortunately this chain of events leads to Atlantis being destroyed and Namor has reforging his alliance to Doctor Doom and now the Atlantean military is based in Latveria (bad), both men join Norman Osborn's Cabal and Namor attacks Tony Stark at the behest of Osborn (also bad), but them Namor (in alliance with Emma Frost) betrays Norman Osborn and joins the X-Men and helps them setup and defend Utopia (good), later he becomes one of the five X-Men possessed by the Phoenix Force (who are all going a bit A God Am I now and the the Big Bads of Avengers Vs X-Men) and stages an unprovoked invasion of Wakanda (very bad).
This Trope could also be named The Black Adam. He started out as a champion of his people in ancient times named Mighty Adam (that's good) then became a brutal dictator and conqueror when his family was killed by a supervillain (that's bad) then millennia later attempted to reform and even joined the Justice Society of America (that's good) then became a not-so-brutal dictator of his country again (NOT the bad part) and later joined a Society of Villains to ensure their safety (that's bad). After said Society betrayed him, he later fought against them when they tried to take over Metropolis (that's good) then went back to being a harsh dictator with plans to form a new Axis Powers coalition (that's bad). When he gained a new family he tried to go back to his old heroic ways and traveled the world fighting evil alongside them (that's good). When this family was killed by supervillains he went on a Roaring Rampage of Revenge, murdered an entire country, and fought every superhero on Earth (that's bad, but awesome). Most recently, his wife Came Back Wrong and started turning his people into dirt and he tried to defend them leading to a truly bizarre situation with Black Adam defending innocents from the corrupted Captain Marvel and Mary Marvel (that's good.) Then he got turned into a statue alongside his wife for his troubles and an oh so ominous shadowy figure wants to make them his champions...(that's bad). At least there's a free choice of toppings (that's good)...that contain potassium benzoate (...that's bad). By the Power of Shazam, that is one busy revolving door.
In addition to having similar personalities and histories of jumping back and forth between good and evil, Namor and Black Adam even look like they could be twins.
Geoffrey St. John from the Sonic The Hedgehog comics is a prime example of one of these. It's even Lampshaded in one issues' off-panel strip.
Rouge was even worse. One story taking place in a single day featured her switching sides at least five times.
Quinlan Vos, a major character in the Star Wars: Republic comic books, is a good example. Here's how he progresses:
First appears as in the Malastare arc as a minor character who operates most efficiently from the shadows, but is nonetheless a respected Jedi Knight (that's good).
Next, he shows up as the main focus of the Twilight arc. Having suffered a complete mindwipe, he's no longer inhibited by the Jedi teachings and resorts to using the dark side to find his missing apprentice (that's bad). At the end of the story, he realises his mistake and submits himself to Mace Windu for retraining (that's good).
Saves the Republic in the Infinity Gate arc (that's good) and gets his knighthood back as a result. Then there's the Darkness arc, which sees him resorting to the dark side once again to fight mutant space vampires (that's bad), but he's able to get himself together again in time to defeat Volfe Karkko (that's good). The next arc which has him as the main character doesn't really feature much of his struggle with the dark side.
Then there's the Clone Wars stories, which sees Vos getting involved in a tangled web of byzantine plans enacted by himself, his Master Tholme and Count Dooku. To become The Mole in Dooku's gang of dark Jedi, Vos fakes a defection to the Separatists (neither good nor bad), killing the information broker who betrayed him in the process (that's bad). While he's there, he proceeds to kill both his Evil Matriarch aunt (who organised the murder of his parents) and a corrupt senator after being convinced by Dooku that he was Darth Sidious, injuring another Jedi Master in the process (that's bad).
Finally appears to resolve his problems once and for all in the climactic Saleucami arc, which shows him defeat the dark Jedi Master Sora Bulq, save the life of Master Tholme and pledge to leave the Jedi to marry his love interest Khaleen after the war was over and raise their child (that's good).
But it's not done yet. Quinlan's final story is set during Order 66, which shows him deciding that he has to survive and kill Emperor Palpatine by any means necessary (that's bad). Ultimately, though, he realizes that his duty as a Jedi is to protect a Wookiee village from the clone commander hunting him, and seems to sacrifice his life to stop him (that's good). He survives, returns to his surviving friends and promises never to let his darkness affect his infant son (that's even better).
So, there we have Quinlan Vos; possibly the only Star Wars character even more conflicted than Anakin Skywalker.
And yet, written in a way that isn't Narmariffic. Arguably, the above list is oversimplifying everything. Most of the time Vos is in the gray area, and occasionally shifts slightly to light or dark.
Luke Skywalker in Dark Empire can't compete with Vos, but he does manage to emulate his dad. First he confronts the Emperor Reborn. Then he realizes that he can't win and joins him, planning to subvert the Empire from within. Then he falls to The Dark Side for real, having very Sith thoughts about killing his Master as soon as he's learned enough - when Leia and Han come to try and rescue him, he captures them and chokes Han. Then, Leia talks him into seeing the error of his ways, so he helps them escape with some important codes before trying to kill Palpatine. Palpatine beat him and bent him back into line - Sith apparently don't mind attempted murder that much, it's kind of expected - and Luke served him and regretted letting his sister go. Finally, he met Leia again, who redeemed him into realizing that he didn't want what Palpatine taught, he wanted to be a Jedi.
In the G.I. Joe comic published by Marvel, Storm Shadow was initially conceived as a mere mercenary hired by Cobra. When his back-story revealed that he was a former student of the same Ninja master that trained Snake-Eyes, he underwent a story arc which involved a reconciliation between himself and his former sword brother. He eventually left Cobra and sided with the G.I. Joe team, going as far as to lead their "Ninja Force" division. During the end of the Marvel run, Storm Shadow was brainwashed into serving Cobra again. The brainwashing was never meant to be permanent, but the comic was canceled before the story arc could be resolved. When the comic was renewed by Devil's Due Publishing years later, Storm Shadow was still employed by Cobra for quite a few issues until he was finally free of his brainwashing and rejoined the Joes for the remainder of the series until the Continuity Reboot.
Raven from Teen Titans, who's turned evil and been redeemed or cleansed of evil about 4 times and counting by now. Most of this has to do with attempts to recapture the success and impact of the first time it happened in the Wolfman/Pereze Titans run. That time it was subtly built up over months. The later ones? Eh, they just sort of happen in a rather transparent attempt to drive up sales. Her Face/Heel turning points almost make her The Millstone of Heel Face Revolving Doors if only for the transparency of her subsequent changes.
Fellow Titan Jericho is just as bad. He started out good but was driven insane by evil spirits from Raven's father's home dimension. After his father killed him to stop his rampage Jericho clung to existence as an evil spirit being. Years later he was revived and purified of his evil. Then he went evil again due to spending too much time in Superboy's clone Match. Now, he's well...kind of a mess to be honest. It's not clear at this time whether he's good, evil, or even functional.
Spider-Man's sometime enemy the Sandman started as a villain, then became a hero and even joined The Avengers. Now he's a villain again, though usually a fairly sympathetic one.
Marvel Comics' version of Ares started as a Card-Carrying Villain who was causing wars and conflicts only because he liked it, but was also fighting alongside other Olympians against a common enemy. Then he realized the other gods would never accept him, went to Earth and lived peacefully among the mortals. Then, when his son got kidnapped, he joined the Olympians in the fight against evil Japanese god Amatsu-Mikaboshi. Later he joined one of the incarnations of The Avengers but often acted like a typical villain towards Hercules. Then he joined the Dark Avengers, a team of villains posing as heroes, and was fighting both good and bad guys as well, while being one of the few members who were treating the heroic part seriously. At the same time he was training a team of killers for Norman Osborn and let his son join Nick Fury, who was opposing Osborn. Finally he betrayed Osborn after finding out he lied to him about Asgard being ruled by Loki and died, fighting alongside Norse Gods he was beating minutes ago.
The Sentry, also from Marvel Comics, goes back and forth between being the universe's greatest hero, its greatest threat, or both at the same time. He's a bundle of mental issues even without factoring in The Void (which is either a Split Personality, an Evil Counterpart that was created when he gained his powers, or his true self), so it's no surprise that his Heel-Face status is as unstable as the rest of him. This is not good news for anyone, hero or villain, when coupled to power that can sunder worlds.
Speaking of Star Wars comics, and ESWU in general, Baron Soontir Fel. He never was shown as a really bad guy, but he switched sides like few others. Let's see — the best Imperial pilot barring Vader (and that's debatable), and receiver of a baronial title, he became quickly disillusioned with Empire and joined Rogue Squadron in exchange to help in searching for his wife, then involuntarily left the New Republic (he was abducted) for a stint in the Empire of the Hand, then served the Chiss Ascendancy (again distinguishing himself there up to receiving the Assistant Syndic position), and then returning to the Empire again, now serving Pellaeon's Imperial Remnant... Let's say that when his children founded a new Empire, it didn't surprise anyone.
Captain Boomerang Jr. from The DCU. He started out as his father's replacement in The Rogues, then tried his hand at being a hero as a member of Nightwing's Outsiders. When he and Dick got into an argument about what to do with Chemo, the living chemical weapon that destroyed Bludhaven, they got into a fight and Owen absconded with Chemo to join the Suicide Squad. In Blackest Night, Owen's desire to be with his father again overrode his morals. He fed people to his zombie father, wrongly believing that this would revive him. Including women and children, which prompted Captain Cold and the other Rogues to kill him. Cold lampshaded Owen's Revolving Door nature, saying he was like a boomerang going back and forth everywhere.
The Enchantress (June Moon) was introcuced in DC Comics' Strange Adventures as a heroine. Then she became a Supergirl villain. Following from that, she became a member of the Forgotten Villains, and then she joined the Suicide Squad, at which point it was established that June was a good person but the Enchantress was her Superpowered Evil Side. In Day of Judgement, Enchantress is an amoral character who has to be pressurised into saving the world from Hell. During this the Enchantress is "killed", leaving June Moon. Later, in a JLA miniseries, they're merged together to form Soulsinger, and then separated again, but the powers stay with June, giving us the heroic Enchantress seen in Shadowpact.
Gary's daughter, Chloe, in The Astounding Wolf-Man. She begins totally supporting her father, then when she finds out he's Wolf-Man, she freaks and doesn't trust him, and after she slowly starts trusting him again, she thinks she witnesses him kill her mother. After this point, she becomes a villain in the series, also thanks to being misled by a former ally Zechariah, who had his own Heel-Face Turn. Eventually, Gary convinces his daughter of what really happened, and Chloe returns to his side.
Red She-Hulk aka Betty Ross has pulled one of those in Incredible Hulk sagas "Super Spy Banner" and "Heart of the Monster". She's a Face for good in the end of "Heart of the Monster".
Dr. Alchemy/Mr. Element (Al Desmond) showed signs of this during the Silver Age of The Flash. He reformed after his first appearances, took up a white-collar job, and became good friends with Barry Allen, even attending his wedding. Meanwhile he was pulled back into evil, or sometimes just framed for it, by everything from Professor Zoom (twice!) to the fluctuations of a distant star to the machinations of a psychic twin (who turned out to be his own split personality given shape post-Crisis).
Marvel's Ghost. He started out as an Iron Man villain, but during Dark Reign he worked against Norman Osborn from within the Thunderbolts and was instrumental in taking him down. Of course, this was immediately followed by him trying to kill Tony Stark yet again. Several times. He's currently one of the most heroic members of the new Thunderbolts, despite trying to kill Tony Stark. Again.
In Avatar: The Last Airbender - The Promise, Zuko seems to be courting an alignment switch (again) from his status at the end of Avatar: The Last Airbender, to which the comic is a sequel. The eponymous promise was made to Zuko by Aang, swearing to take him down if he ever started acting like his father. Throughout the comic, he becomes more and more obsessed with protecting his people and the many assassination attempts he's undergone, and the last panel of the first volume has him seeking advice from his father in prison. And we know that he makes yet anotherHeel-Face Turn by the end, since The Legend of Korra info has already confirmed he and Aang found United Republic together.
Due to his simple and unstable psyche and tendency to go into blind rages, The Incredible Hulk has gone from hero to villain and back again his entire existence. For instance, Hulk will save a city one minute, then someone (typically his nemesis General Ross) will piss him off and he'll start ripping apart the city he just saved. In the end though, Hulk will usually end up doing the right thing, even if it's just by accident.
Speaking of Ross, he himself tends to go through the door over and over depending on how obsessive and what lengths he's willing to go to bring down Hulk that issue. Sometimes Ross is willing to help Banner be cured of the Hulk or leave him be for the moment if he does something good, other times he's been out to straight up murder Banner from the outset and nothing will deter him from it. He eventually joined The Avengers as Red Hulk, but left to form the new Thunderbolts after becoming dissatisfied with their methods.