In a Daredevil story from early in Frank Miller's run, DD is the only hero available to stop the Hulk from hurting anyone during one of his rampages. Naturally, Daredevil is completely outmatched, and the first few minutes of him facing the Hulk leave him badly wounded and forced to retreat to catch his breath. During this, Matt contemplates fleeing as he realizes how impossible his odds are, and nobody else would know that he turned tail and ran — except for himself. Refusing to flee like a coward, he goes back and faces the Hulk and gets him to stand down in spite of his injuries.
The Incredible Hulk (1968): During the "Over the Edge" crossover with The Punisher, the Hulk refuses to help Nick Fury because of SHIELD's previous mistreatment of him. When it looks like Castle has successfully killed Nick, Hulk's guilt-wracked.
Spider-Man: This is one of the running themes of the series.
Peter Parker is unique for the fact that he became a superhero because he failed this test. After getting superpowers on a silver platter in Amazing Fantasy #15, he tried to cash in on them and had no grand plans aside from using the money to provide for his family. But then a burglar passes by and he does nothing and when called out for it, exclaims that it isn't his job. That burglar then killed Uncle Ben, i.e. his beloved surrogate father. This moral failure and lapse pretty much defines Spider-Man for the rest of his life, and his attempts to do good and redeem himself.
Something a lot of people forget is that the very first life Spider-Man ever saved... was John Jameson, J. Jonah Jameson's son. Contrary to popular belief, Peter did not immediately become start fighting crime after the death of Ben Parker; his first concern was that his Aunt May was facing financial ruin without her husband's support, and he tried to earn money for her not by immediately joining the Daily Bugle, but by performing stunts as Spider-Man for paying audiences. It worked right up until Jameson started running his soon-to-be-standard slander accusing him of being a menace, shutting down any future shows. When Jameson's test pilot son is about to be killed in a rocket-test gone wrong, however, Peter is in the audience; how many could honestly say they'd risk their lives to save the son of a man who was even then ruining their life and the lives of their loved ones? Doesn't stop Spider-Man from riding a jet into the air, web-slinging onto the falling rocket mid-flight and attaching the part that will fix the problem, going down in history as his first truly selfless act of heroism.
Inverted in a Secret Wars II crossover. The Beyonder has transformed a skyscraper into solid gold. Spider-Man realizes that all of his financial woes would be solved if he takes even a transformed gold notebook. No one would ever know. So he takes it. However, he winds up wracked with guilt over it, which is ridiculous since he has literally saved the world dozens if not hundreds of times for free while living on what amounts to a subsistence lifestyle. He doesn't get over it until Black Cat steals the notebook from him.
In The Amazing Spider-Man (2018), Peter cites his refusal to turn in his unearned degree after his revival in his own body as another failing of a similar kind. He notes that after getting his body back he simply walked past a wall showing his graduate degree earned by Octavius in his body and he didn't turn it in and realizing this, he comes to the conclusion that the plagiarism scandal he faces is entirely deserved and justified.
In The Amazing Spider-Man (1963) #237, Stilt-Man is desperate to achieve something and plots killing Spider-Man to earn some street cred. However, during the fight Spider-Man saves him from a laser beam which accidentally knocks him out. Stilt-Man realizes that they are alone and Spider-Man is defenseless. He just could murder him and claim he killed him in a fair fight, and nobody would ever know the truth... nobody but him, that is. So he does not go through with it.
Peter Parker experiences this early in his career (in The Amazing Spider-Man (Lee & Ditko) #5) when his high school bully, Flash Thompson, dresses up as Spider-Man in a failed prank attempt and is captured by Doctor Doom by mistake. For about half a panel, Peter considers doing nothing, letting Doom take care of his problem for him. He then realizes that he could never let Flash come to harm, and Spider-Man heads off to the rescue.
Back during the original run of Thunderbolts (when everyone still believes the disguised villains to be heroes) Spider-Man is framed for murder, and the T-Bolts are assigned to apprehend him. At first, MACH-1 (who was formerly Spidey's enemy the Beetle) relishes the thought, but after he and the rest of the team fight alongside Spidey against the true threat, he throws away the chance to make the charge stick and get away with it, giving Spidey the evidence that clears him. He tells Baron Zemo he did it so Spider-Man wouldn't be suspicious and risk their covers but that's not the real reason. Why? He realizes he's supposed to be the hero, and after teaming up with his old foe, it's starting to grow on him. As he tells Moonstone on the last page of the comic, "This hero stuff... I think it's starting to become contagious..."
During the events of Ultimatum, Spidey risks his life after the flooding of New York dragging people to safety, which J. Jonah Jameson witnesses. The event causes JJ to actually stop writing anti-Spidey headlines, having been humbled by what he witnessed (and amazingly, this sticks).
A few months later, during the events of Ultimate Enemy, Spider-Man and Spider-Woman are inside Roxxon as the building is being crushed by a tentacle monster (long story). As they're fleeing, they find Doctor Octopus pleading for help. This is a man who has previously tried to ruin Peter's life out of sheer spite. Spider-Woman advocates just leaving him to his well-deserved fate, but Peter refuses. As with Jameson, this act causes Ock to make a genuine Heel–Face Turn.
Subverted in Ultimate X Men. During a mission to the Savage Land, Wolverine and Cyclops are alone, out of contact with the team, and Cyclops is dangling over a crevasse. Wolverine could easily let him drop and no one would ever know the truth. So he does. And he doesn't feel bad about it either. Then he goes home and tries to get together with Jean. Of course, Cyclops survives.
In their first meeting, Thor spooks Banner by telling him he is aware that Bruce cries every night over Betty's rejections, and that he fantasizes about hurting the Pyms for getting his old job.
In public, Henry Pym is all nice and all smiles, but when nobody is watching them, he is a violent domestic abuser. Even before this comes out, some of Henry's inner nastiness peaks through.
What If?: In "What If Doctor Doom Had Become A Hero" ends with a very brutal one. This version of Doom who avoided being scarred is eventually successful in not only becoming the shining hero his mainstream counterpart always claimed he would've been, but also manages to free his mother's soul from Mephisto, something our Doctor Doom had failed at, which gets Mephisto royally furious with him. On the night of his wedding, Mephisto traps all of Latveria in a glass ball, and hands Doom his royal ass, before presenting him with a Sadistic Choice: Either his soul takes the place of his mother in exchange for Latveria's freedom or his wife Valeria's does. Presented with either saving his wife or being able to continue improving the world through his genius, Doom lets his wife be taken to Hell. "The world must not be deprived of Doom." Credit where it's due, he spends the rest of his life battling the forces of Hell one night every year to try and get her back, and the ending leaves open the possibility that he might someday, but even as a hero, Doom's Pride and belief that the world simply can't get on without his brilliance will always come before anything else, no matter what he claims.
