Marvel's Civil War storyline featured the superheroes favoring registration fighting the superheroes opposing it. Apparently, the two sides were supposed to be presented evenly but due to the clear Aesops of the last century saying that secret identities are good and government oversight of superheroes is evil, it was hard to sympathize with the Pro-Regs. Especially since Iron Man, the Pro-Reg leader, became a borderline Fascist Nazibot for most of the storyline. The whole thing was basically a titanic Idiot Plot where everyone held the Conflict Ball.
The X-Men in particular stayed out of the entire debate surrounding the Super Human Registration Act since in their own comics, government registration of mutants was always portrayed as the first step towards state-sponsored internment/genocide of anyone with an X-gene.
In JLA: Act of God there is an underlying implication that the superheroes were being punished for their arrogance. Even though people like Superman and Wonder Woman are fairly humble in normal continuity (not to mention all the characters who are nothing but humble, such as Captain Marvel), while Batman in this story is ego tripping and denigrating the contributions of his formerly powered friends even as they kiss his ass. Apparently the writer thought the superheroes WERE being arrogant because they weren't bowing at Batman's feet and worshiping him as the greatest superhero of them all. This requires the aesop not to apply to Batman, because he's the single most arrogant person in the story.
Really, the whole arrogance thing just utterly falls apart the MOMENT the event begins because heroes are shown losing their powers WHILE TRYING TO SAVE LIVES. It's not like we see Green Lantern showboating or Hawk Man demanding praise, we're treated to Superman losing his powers while trying to hold a dam together and Flash slowing down while trying to intercept a bullet aimed at a cop... Then being told it's probably for their own good.
Also, there's a comment about Supergirl's actions as a superhero was an abuse of power, acting outside the law, only to disregard this and comment about how inefficient police work is and how much more effective she was as a superpowered vigilante and how she should go back to being a vigilante. Then it breaks that aesop because standard police work (like forensics) did more to uncover what happened to The Atom than vigilantism.
Marvel AdventuresSpider-Man # 39 has a foreign exchange student named Kristoff show up at Peter's school, and make a speech about how, unlike many of his countrymen, he doesn't hate America. Peter shows him around, and they talk until it's revealed that Kristoff is from Latveria, home of Doctor Doom. Peter freaks out a bit but accepts him for it. Then the Fantastic Four show up, attacking Kristoff seemingly just because of his Latverian origin, calling him a "potential threat to national security", and taking him away. So, it turns out that he's just a normal, nice kid and the Aesop is that ethnic prejudice is wrong, right? ... well, no, because it turns out that he was Actually a Doombot, and Spidey and the FF have to beat him up. So, the Aesop is that you should never trust people from enemy countries, even when they seem to be perfectly nice, and that it's totally logical to seize and search people who might be a problem.
Mystery in Space #8 featured the story "It's a Woman's World!", in which a man stuggles to prove himself in a future where women have dominated society. It appears to be a story about gender equality, but then you get to the very end, in which the male protagonist forces his wife to do housework, and the wife in turn admits that women ran things long enough and that men should take over again. The story, of course, was published in 1952.
One More Day breaks the aesop that Spider-Man is supposed to embody, as instead of taking responsibility for his actions, he dodges it by making a Deal with the Devil against the wishes of its main beneficiary and guilt-tripping his own wife into going along with it. However, in One Moment in Time (popularly known as OMIT), this is retconned so that Mary Jane is the one to have made the deal. Word of God is that the aesop is meant to be "It's heroic to do whatever you can to save a life" but to readers, rewriting history just to save the life of a single person who, in addition to wanting to die anyways and was telling you to let go, let's face it, is likely to die of old age in a few years is simply asinine. The message then becomes "the ends justify the means", and that instead of learning how to cope with loss and move on with your life, you should hold on to what you have and never let go, even if the cost of doing so might be too high, for you and for others.
The Sandman has a rare in-universe example. The Kipling-quoting "Indian Gentleman" tells his companions a tale he hopes will "prove" that women are inherently evil in "Hob's Leviathan." But the men in the story are no angels themselves, and as his shipmate Hob points out, the sum Aesop of the story seems to be more along the lines of "men and women are both capable of deeply hurting each other."
Superman: At Earth's End has one of these. Superman loses (most of) his powers and has to rely on a gigantic machine gun to solve his problems. After using his gun to kill two Hitlers and a Batman zombie (don't ask) he tells his allies (some little kids with guns) that he's dying. The little kids then bawl and say that guns killed Superman before throwing all of their guns into a bonfire. Of course, no one bothers to point out that guns also saved the kids from two Hitlers and a Batman zombie!
Worse is the fact that Superman himself admitted that the only thing keeping all these kids alive in this After the EndGOTHAM was those guns.
Batman, for God knows what reason, has the gun that killed his parents proudly displayed in his batcave - it's even labeled "THE GUN THAT KILLED MY PARENTS". For someone who despises guns like Batman does, it makes you wonder why he spent time locating the gun in the first place.
Uncanny Avengers is the first real attempt at a team book that has the Avengers forming an alliance with the X-Men in the name of promoting diversity and tolerance for the mutant condition — and in some eyes, it's fallen flat on its ass. Issue #5 has Havok give a speech that could be taken to say, "I want to be seen as more than just 'that mutant'"; however, given the wording, many have taken it as saying, "Merely adopting a cultural identifier such as 'mutant' is a divisive gesture that separates us from others." It's not helped by Issue #9, which features such greatest hits as "Members of the majority don't understand why minority puts so much stock in cultural identity" and "Being born with a certain condition isn't a real cultural identity."
Usagi Yojimbo plays this one for laughs. As a young man, Usagi's teacher Katsuichi enters Usagi into a tournament at the local dojo. The following conversation is held before Usagi's first bout.
Katsuichi: Do you remember what I taught you? Usagi: Yes, sensei. I am here to test my skills, not necessarily to win. Katsuichi: And? Usagi: "Spirit and inner strength are essential. Winning is unimportant!" Katsuichi: And if you don't win? Usagi: You'll beat me to a pulp! Katsuichi: Hah! You've learned well.
Despite trying to lecture the world about how great mutants were and how they should be allowed to embrace their identities, Xavier spent most of his life masquerading as a normal human who just happened to be a mutant expert. Xavier only involuntarily "outed" himself during Grant Morrison's New X-Men run when he was possessed by his evil twin.
James McAvoy said he actually kept this in mind while portraying Xavier in X-Men: First Class. He pointed out that Xavier is a well-meaning, but ultimately misguided liberal, as he still has tons of societal advantages given that he's white, heterosexual, male, and extremely wealthy. He certainly doesn't have to put up with the same bigotry many mutants face (hell, the same bigotry many real world minorities still face), which causes his message of peace to ring if not false, at least simplistic to many.
Also, compare Xavier's powerset to those of characters like Rogue, Toad, or Cyclops. Xavier has telepathy — a power that he can control perfectly, that has absolutely no negative effects on him physically or mentally, and that is a massive benefit to his life. In comparison? Rogue's powers kill anyone she has physical contact with. She cannot control this or stop it in any way, and has resigned herself to being isolated from her peers. Her powers have drastically injured her self-esteem and social life. Toad's mutation turned him into an ugly, lizardlike humanoid and made him the subject of severe bullying from other children. Cyclops projects a continuous wave of destructive energy from his eyes and relies on special glasses just to live a normal life. Even Phoenix, another telepath, is often overwhelmed by the thoughts of others — to the point of mental instability. Looking at the general trend of mutant powers, it's hard not to think that Xavier really lucked out where the Superpower Lottery was concerned.
Furthermore, even if you ignore evil mutants who use their powers for terrorism, it's not uncommon for a mutant's powers to get out of control and end up hurting or killing a lot of people or causing a ton of property damage, giving humans a valid reason for not wanting them around. Even worse, for all their talk about wanting equality with mankind, we almost never see the X-Men try and welcome regular humans be around them. And they don't really try to make the few humans who do try to be around them feel welcome. For example, the Xavier Institute once employed a regular human nurse named Annie. At one point when they needed her help with a group of crucified mutants, Jean Grey used her telepathy to call her and was annoyed when she panicked after hearing Jean's voice in her head without any warning and the group talked down to her for being human. Similarly, after M-Day, many mutants lost their powers, including members of the New Mutants and other X-Men affiliated teams. What was the X-Men's response to this? Oh, sorry, you're not a mutant anymore so we're not going to help or protect you anymore. Many newly-powerless former mutants were booted from Xavier Mansion, often with the only place for them to go to be return to their abusive parents. They were promptly captured by anti-mutant extremists and most were murdered.
In continuities as old as Marvel and DC's, the inevitable retcons often break initially intact aesops. For example, many of the older X-Men storylines involving Nightcrawler made it anviliciously clear that Fantastic Racism is bad, that we shouldn't judge people by their external appearance, and that having a tail doesn't necessarily make you the Antichrist. Enter Chuck Austen, and it turns out Nightcrawler really was half-demon all along.
Batman: War Games, and its follow up War Crimes seems to have the aesop that teenagers shouldn't be superheroes, because they might screw up and get killed. Except, despite the brutal death of Spoiler, both Tim Drake and Cassandra Cain (who were the same age as Stephanie) continue to operate, except now they move to Bludhaven, a city that is worse than Gotham. On top of that, Steph's actions were in response to the emotional abuse Batman put her through ever since he met her (namely, repeatedly taking her under his wing then firing her and telling her she's terrible for making the same mistakes he forgives the boy Robins for), on top of her already present issues with wanting to prove herself, and she was only able to cause the gangwar that lead to her death because Batman, despite firing her, then gave her unsupervised access to his computer where he kept his contingency plans (while never giving her the information she'd need to do them right, info that even Catwoman knew, stuff he should have given to her while she was Robin), basically meaning Batman took an emotionally vulnerable young girl, made her more emotionally unstable, then gave her the tools to either fix or destroy the city without the knowledge on how to use them. Essentially, the aesop isn't so much as 'kids shouldn't be superheroes', its that 'kids should only be superheroes if Batman likes them'.
Zipi y Zape: Several, usually courtesy of the twins' parents. For example: Mr. Pantuflo has promised, several times, that if their twins get an A he will buy them a bike, the object of their desires. They got an A once (they got As quite frequently in fact), not because of any academic prowess, but they got it fairly. So Mr. Pantuflo was obliged to "buy them what they wrote on a piece of paper" they gave him before. The paper was, predictably, full of typos ("We wan a visikle wit too weels") so Mr. Pantuflo said "I don't know what a 'visikle' is, it's not in the dictionary - so I'm not buying it." Kids, don't bother being a good kid: unless your spelling is good, your parents will screw you on a technicality.