Iron Man during the Civil War, with Captain America as the Designated Villain, Depending on the Writer. In some issues from that arc, the exact opposite effect occurred: Iron Man appeared to be the Designated Villain (to many, he seemed like a reasonable guy defending normal humans against powerful forces while trying to avert a backlash against superheroes, yet some writers expected us to root against him) and Cap seemed like the Designated Hero (refusing to take seriously Iron Man and Reed Richards' arguments that humans were in danger due to the mega-powerful supers running loose and unaccountable, yet some writers expected us to find Cap to be completely reasonable). The fact that the writers themselves seemed to be fighting over which side was right just added to the confusion; some sources claim that there wasn't actually a single, mutually-agreed version of the letter of the Super Registration Act, which surely cannot have helped.
Perhaps the Aesop was that neither extreme was truly moral. If that's what they were going for, designated heroes were the way to go. Captain America was the Designated Hero more often than not with Iron Man as the Designated Villain. Mainly because the politics associated with Cap's side tended to resonate better with most of the writers. But all in all, it was a case of a complicated issue being "simplified" by having a good guy and a bad guy. Iron Man and his pro-Registration side all took a big hit in the credibility department when they started tossing anti-Registration heroes into a parallel universe prison without trials.
Another example of Iron Man being the Designated Hero was World War Hulk. To the point where many readers were cheering the Hulk on. (This was, in fact, already happening when Civil War was still going on, with "You're all fucked when the Hulk gets back!" being a common response to Marvel's ad campaign trying to get fans to choose a side in the war.)
According to Word of God, the official stance is that Iron Man and the Pro-Registration side was meant to be the one in the right; and they thought it was "so obvious" (despite "Registration" in Marvel comics historically relating to "Mutant Death Camps", and despite Captain America traditionally being the moral compass of the Marvel universe) that they threw in a few Kick the Dog moments to make it seem more ambiguous. If so, they went seriously overboard, since the Pro-Reg does things like try to arrest Cap by force for breaking the Act before the Act was even passed, creating clone of Thor that went Ax-Crazy and killed an Anti-Reg C-list hero (Bill Foster/Goliath), hiring supervillains to capture their opponents (and giving the Ax-Crazy mass-murderer Norman Osborna major position in SHIELD), throwing captured heroes into a prison without trial in the NEGATIVE ZONE (an otherworldly post-apocalyptic dimension populated entirely with dangerous aliens and monsters) and trying to start a war with another nation (Atlantis). The worst the Anti-Reg side did was hire The Punisher (then fire him immediately), fight Pro-Reg forces, and be on the receiving end of Straw Man Political journalism. The majority of readers sided with Cap and supporters of both sides thought Iron Man was a dick in this story and believed he was meant to be the bad guy.
And then he and Reed Richards (two of the heads of the Pro-Registration faction) use science to make everyone forget Spider-Man's secret identity so he can continue being a vigilante without having to deal with accountability in One Moment in Time. Which pretty much goes against what they fought the entire Civil War and committed all their crimes against humanity to put a stop to. So you can add horrific levels of hypocrisy to the list of what makes them designated heroes.
There was a lot of this in Avengers vs. X-Men as well. Depending on the Writer, Captain America and the Avengers are a bunch of fascists jerks to the plucky underdog X-Men, or Cyclops and his X-Men are a bunch of religious fanatics and dictators waiting to happen.
The aftermath is just as confusing with regards to this trope. Cyclops is definitely framed as being in the wrong (it was him who killed Professor Xavier, after all), but the validity of this is pretty questionable considering why he killed Xavier and that he was spurred on by the Avengers, but other issues have members of the Avengers calling out Tony Stark over his role in the crisis. The fact that the Avengers were the ones to man up and offer the olive branch to the X-Men just confuses the roles even more.
Throughout the series and aftermath, the only one who seems to be constantly a Designated Hero is Wolverine, who essentially causes the conflict by telling Captain America what essentially amounted to biased accounts on Cyclops' character and the Phoenix as a whole, repeatedly attempts to kill Hope because 'it's the only way' to stop the Phoenix (which would have fucked everything up had he been successful), and afterwards doesn't even try to help the newly appearing, and vulnerable, mutants. He does however, find the time to harass Cyclops at every opportunity when he tries to do so.
Sam and Max are ostensibly peacekeepers, but in practice they're peacekeepers who are only happy if there's no peace to keep, and the latter of the duo is a sociopathic maniac who's more of a mobile and highly unstable weapon than a detective. In Max's words, they save the world. Sometimes on purpose!
One of Steve Purcell's rules for writers in other Sam and Max media is that while Sam and Max are sociopaths, they're still HEROIC Sociopaths. Heroic sociopaths with a wing in Hell dedicated to them. That are allowed into Heaven. Make of that what you will.
Nemesis the Warlock is supposed to be seen as an hero of the alien resistance, but is really a manipulative, murderous jerk and nobody would root for him, was he fighting somebody less evil than Torquemada. Later the series decides to turn him into one in-universe, revealing some unpleasant things about him: most notably, that his motivation is simple boredom and he could have solved the conflict long time ago, but is holding back, therefore prolonging a monstrous war, that took a great toll on both sides and caused the genocide of countless alien species as well as the deaths of his wife and son, for thrills. That however makes him lose the status of a hero among both his allies and the readers.
Gladstone Gander in The Sign of the Triple Distelfink. Considering the immense lucky streaks he gets every other day of the year and his unrelenting smugness about that fact, it's hard to feel sorry for him if his Born Lucky status is inverted on a single one. And he accomplishes his goal of getting rid of even that blot on his entitlement to fortune, while beating Donald out of attaining any luck for himself, who is usually portrayed as barely being able to get by or financially support his nephews (take for example the ending to Super Snooper Strikes Again).
A common problem with the '90s Anti-Hero trope is that they might end up this when badly handled. Countless comics had the hero smashing into a doom fortress and butchering dozens of mooks, without explaining why he's there, who the mooks are, or what he actually wants - about the only way to tell is to check if he's on the cover.
Things become more complicated and worse when it is revealed Mary Jane egged him on and her reasons why.
In Gold Key Comics Star Trek story The Planet of no Return, aka K-G, Planet of Death, Kirk and co. discover a planet with a plant civilization, in an otherwise uninhabited galaxy. Unsurprisingly, the plants view the landing party as prey. To prevent this civilization, which was just sitting there minding its own business, spreading to neighboring uninhabited planets, Spock performs an act of planet-wide genocide. We even get to see the Enterprise phasering sentient trees who burn as they run for their lives across a devastated landscape.
Batman, if not handled properly, can fall into this category. This is especially apparent in some of Frank Miller's later work. For example, in All-Star Batman and Robin, he outright kidnaps Robin, roughs up Alfred for daring to give the kid some food rather than forcing him to eat rats, gloats about his intellectual superiority to Superman, in general demonstrates little compunction for killing or abusing other heroes, and does barely any actual crimefighting.
The Fixer from Holy Terror (who, interestingly enough, was written by Frank Miller and was a Captain Ersatz of Batman). Natalie Stack is at least a criminal already, but The Fixer is meant to be the hero of Empire City. Said hero yells at his allies and belittles them, uses guns on the terrorists, cripples one and threatens to gouge his eyes and blows them up despite saying he despises their lack of respect for life, makes constant racists remarks about them and doesn't suggest any other method of stopping someone save for killing, including a corrupt police commissioner. And before the comic ends, he reveals he only fights crime to stay in shape and practice on criminals to get ready in case of a terrorist invasion, meaning his only interest has been to kill Muslim terrorists.
The Authority came to be this in later issues, being treated as heroes despite doing horribly amoral things (Midnighter paving through a bunch of civilians to take out a villain or stopping an invasion from a parallel Earth by destroying a whole country, even though it is clear that the invaders are completely outmatched anyways). Under the pen of series creator Warren Ellis this was deliberate as his vision of the Authority was that they were supervillains being used to take down worse supervillains. However when Mark Millar took over they were turned into his political mouthpieces and thus were always presented as being in the right, even when they committed terrible atrocities in the name of peace.
Black Canary and Dick Grayson are supposed to be seen as trying to help Roy when his grief over losing an arm and losing his daughter Lian cause him to spiral back into drug addiction while also becoming a violent anti-hero. The problem is just that they do more damage than they fix. Black Canary spends most of the arc looking like she's made of ice, and ultimately decides to wash her hands of Roy, considering him a lost cause. Dick abandons Roy in a center for villains with substance abuse problems, and does nothing to argue with Canary over her condemnation of Roy. As a matter of fact, Canary's behavior is called out in Birds of Prey when she's subjugated to Mind Rape by a villain forcing her to relive her past mistakes. An illusion of Roy specifically asks how she could let him become "this thing" he is now.
Donna Troy, Wally West, Cyborg, and Doctor Mid-Nite are equally unhelpful. Donna and Wally do nothing to help Roy, Doctor Mid-Nite is completely ignorant of how badly hurt Roy really is when he begins stealing pain medication and Mid-Nite never catches on, and Cyborg gives Roy a shoddy prosthetic arm that causes even more pain while making inappropriate jokes about the situation.
King Aspen and his deer (except Bramble) from My Little Pony: Friendship Is Magic (IDW), despite being presented as victims losing their home to an evil construction company, came off as much more heartless and villainous than Well-To-Do. While Well-To-Do unrepentantly destroyed a chunk of the forest, King Aspen caused much more damage by sending vines and animals from the forest to invade pretty much all of Equestria and endangered countless innocents who had absolutely nothing to do with it out of mere petty vengeance. Not only did these actions actually prolong the problem (Celestia and Luna would have happily helped if they weren't busy defending Canterlot from the vines), but the deer are completely unapologetic about it and not even so much as told off for it (Can't Argue With Deer, after all) . The comic even ends with Princess Celestia apologizing to them for some reason. To say this all hit a sore spotwith the fanbase is one heck of an understatement; the fanbase's description of the deer tends to fall somewhere between sociopathic smug elves and eco-terrorists.
Due to extreme Values Dissonance, basically every "good" character in Chick Tracts up to and including God. The measure of what constitutes morality in the Chick Tracts universe is based solely on devotion to Chick's own brand of extreme cultish fundamentalist evangelism, which the vast majority of Christians, let alone people in general, simply do not share. Characters can be the most selfish, cruel and just plain awful human beings to ever exist, but a deathbed conversion or lip service to the author's professed religious beliefs will have them ascend to heaven, while people who spent their entire life trying to stop misery around the world will go to hell for the crime of not bothering to convert anyone.
God himself comes across as a cruel, petty and nasty egomaniac who doesn't care about mankind and hungers only for adoration.
Kingdom Come intentionally invokes the trope as part of its satire of Nineties Anti Heroes, which were popular around the time it was written. The story displays an alternate universe where the anti-heroes have evolved into full-on designated heroes after Superman retires; they quickly kill all the villains, and then, bored, turn on each other. The end result is that we open In Medias Res of a world where the costumed neo-fascists, Bomb-Throwing Anarchists, Torture Technicians, and Right Wing Militia Fanatics gun each other down in the streets for nothing more than amusement, all the while still having the gall to call themselves "heroes."
Solstice was a generally heroic character... until she murdered a judge. She does this so she can be incarcerated with her lover Bar Torr, but it's played as a sad ending for her and the characters sympathise and say it's wrong she's incarcerated. As opposed to, say, exactly what she deserves for, again, murdering a judge.
Bunker got this big time in Will Pfeifer's run. He saves a bunch of people from an incident, and one of the guys says that, of all the heroes they're saved by the two that look like... we'll never know what he was going to say, because Bunker slams the dude into a brick wall assuming he'd say something homophobic (Bunker himself is also gay). We were obviously supposed to side with Bunker as he dressed down this guy afterwards, but people ended up siding with the guy since he was being brutalised for being ungrateful. Yeah, not exactly heroic behaviour right there.
Civil War II gives us Captain Marvel, following in the footsteps of Iron Man in the first Civil War and who went a little crazy with her methods while using a Inhuman precog to combat crimes. She went around trying to arrest her allies and others for things that haven't happened yet, and ignored people when they tried to tell her that the precog wasn't really seeing the future, at least not with 100% accurately. Having indirectly caused the deaths of War Machine and Bruce Banner, she grew more stubborn in her beliefs and went on to imprison an innocent woman, tried to arrest Miles for a crime he may not commit, and put Iron Man in coma when he opposed her.While some fans still love the character, others are unsure that she should be the female face of Marvel.
Inhumans vs. X-Men has the Inhumans, who are trying to stop the X-Men from essentially saving their people from being gassed by their Terrigen Mists, all so they can continue using those self-same mists to forcibly convert people with Inhuman ancestry into new Inhumans. Needless to say, having people die for their own benefit isn't heroic. And it only gets worse when supplemented by Death of X and the tie-in volumes of Deadpool and the Mercs For Money, both of which prove that to the Inhumans, the Terrigen Clouds are so sacred that they outweigh mutant lives in their eyes.
In the Death of X, it's revealed that Black Bolt executed Cyclops for the hideous crime of... altering a Terrigen Cloud to still function as it should whilst no longer being lethal to mutants. Although Inhumans vs. X-Men tried to retcon that this caused the Cloud to destabilize and fall apart, that wasn't presented as being the case in Death of X, and it still presents Black Bolt in a terrible light, since he still executed someone.
In Deadpool and the Mercs for Money, meanwhile, the characters visit an Alternate Universe where the X-Men had one of their Reality Warpers successfully transmute the Terrigen Clouds to be harmless to mutants and still function to power-up Inhumans. The result? The war between the two races got worse, as the Inhumans were outraged that the Terrigen Mists were no longer 100% the same chemical makeup as they had always been.
This is even more obvious when one looks at the prior history of the Inhumans, which made it clear that they were largely Anti Heroes at best; the noble class of an intensely stratified and isolated monarchy with all the problems that comes with it, including archaic rituals, intense xenophobia, imperialistic ventures, and even slave labor at points. Trying to switch them to being straightforward protagonists was really never going to work.