Spider-Man gets a lot of undeserved flak, mostly due to the negative PR campaign by his employer, J. Jonah Jameson. Probably the first superhero to have this as his status quo.
Within the first twenty issues it was revealed JJ felt jealous of Spidey's successes. Later revelations included being beaten by his stepfather, a mistrust of superheroes, and JJ's own failure to live up to the high standards he sets for himself. In Spider-Man: The Animated Series, JJ hates Spider-Man because he wears a mask, and his wife was killed by a masked man.
Though he is always the first to accuse Spider-Man of crimes, JJ is also usually the first to retract his statement when he is proven wrong, at one point remarking that he believes that claiming Spidey to be a menace prevents him from actually becoming one. Furthermore, regardless of the Daily Bugle's libel, there is enough evidence to suggest that the New Yorkers are not so easily manipulated anymore and will rally behind Spider-Man.
Jameson eventually became the Mayor of New York City — and as you might expect he constantly leveraged his expanded sphere of influence against Spider-Man.
There is the fact that Peter began his superhero career as a teenager with no guidance and tended to be a wisecracking jerk who often screwed up and lost, and also tried more than once to draw a paycheck for it (nobody knows he needs the money to take care of his aunt). A bad first impression is hard to shake. Plus, being immature, he tended to egg on JJ or get angry at him (which could be interpreted as threatening).
Interestingly, while the public and the police are quick to believe the worst about Spider-Man, and his "friends" in the superhero community rarely if ever stick up for him at all, it has been shown on several occasions that most of the villains in his Rogue's Gallery know he is a decent man and innocent of just about everything he's accused of. This was highlighted in an early issue of Thunderbolts, when Spider-Man was accused of a crime and the team of villains-pretending-to-be-heroes was trying to develop a plan to capture him in order to get good publicity. Mach-One, who was really the Beetle in disguise and had fought Spider-Man many times, told the team that the best thing to do was to go to the scene of the crime and wait for Spider-Man to show up and start investigating himself. When asked why he was so sure Spider-Man would do that, Mach-One responded with: "Because he's innocent. He'd never do anything like this. He'll be looking for the person who did." During this same issue, Mach-One fought alongside Spider-Man and was so impressed that this event was the beginning of him trying to turn his life around and become a real hero, which also spread to several other members of the team.
In Superman vs. the Amazing Spider-Man, Superman initially thinks Spidey may be connected with a phony Superman because of Jameson's smear. Supes realizes his mistake right away, though.
Perhaps one of the biggest reasons why Spider-Man gets a lot of publicity (particularly the police force) is his total unwillingness to kill the supervillains that he fights against. In fact, in Superior Spider Man, Otto Octavius inside Peter Parker's body, manages to win public support by killing Massacre. Something that Peter Parker himself is unwilling to do because he's aware of the moral hazards. Apparently, the public isn't really happy about Spidey fighting a supervillain, sending the villain to jail, only to escape again and commit crimes that are worse (something that Otto himself pointed out to Ghost Peter). Because apparently, the governments inability to execute/ permanently incarcerate villains is totally Spidey's fault..
During The Amazing Spider-Man (2018), J. Jonah Jameson makes the argument that Spider-Man's bad public image is, at least in part, his own damn fault; while most other superheroes tend to work in teams and communities and are fairly open with the public, Spider-Man is usually a lone wolf and frequently gets into fights with other superheroes before teaming up with them (though as Peter points out, this is very common for other Marvel superheroes). Furthermore, whenever Jameson made a false accusation against Spider-Man, the Wall-Crawler's response was never to reach out and set the record straight but rather to insult, antagonize and sometimes even threaten Jameson, which does not help his case at all.
In the Ultimate line of Spider-Man comics, JJ initially only wanted to make headlines. This quickly changed, however. It came to a head after The Bugle publicly started to support Sam Bullit, who was running on an anti-vigilante (in other words, anti-superheroes) campaign. But later, after an attempt on his life by some of the Kingpin's goons, JJ went to Peter's house (after having fired Peter from his job at the Daily Bugle earlier) and revealed his deeper reasons. He'd launched a smear campaign against Spider-Man because he didn't like the fact that his own son, who had died in a space shuttle accident (a real hero in Jameson's eyes), wasn't thought of as one and didn't get the attention he deserved, while everyday people looked up to a guy swingin' in his underwear.
Finally inverted later on, though. After Jameson sees Spider-Man risking his life to save a woman during a flood, he does a total 180 and devotes the Bugle's energies to supporting him.
In fact, after the Ultimatum wave, Jameson becomes one of Spider-Man's greatest advocates. For instance, when he discovers Peter's identity, he uses the information to clear Spider-Man's name without revealing his secret identity. He then gives Peter his job back and offers to pay for his college tuition. Eventually, when Spider-Man dies, he attends the funeral and comforts Aunt May in her time of need.
Humorously, the alternate future of Marvel Comics 2 sees JJJ as a big fan and major supporter of Spider-Girl, the daughter of the hero he had slandered.
This is exaggerated in Ultimate Spider-Man (2012) where Jameson's smear campaign is not only more effective, but less deserved as he's become an agent of S.H.I.E.L.D. and has never egged-on JJ, thus giving less credence to it. The beginning of Season 3 finally averts this. Spidey joining and becoming a successful Avenger results in the general populace of New York loving him.
Apparently, it comes with the webs, because across the Multiverse it's revealed that numerous Spider-Men/Women/Girls have this going for them. Spider-Gwen is wanted for the murder of her Peter Parker and has drawn gunfire from police officers. The steampunk Lady Spider has been labelled a menace by J. Jonah Jameson in her world. Spider-Man Noir isn't much loved where he comes from. And they're all bouncing aroundthe multiverse filling in where other Spider-Men were killed or lost and finding themselves not necessarily welcome. It's even revealed in one comic that they only reason they even became Spidermen in the first place was because of their bad reputations coupled with with an attitude ultimately willing to put up with it, being the Chosen One by virtue of keeping their anger of the unfairness of society towards them in check; heroes who will do right for the world even if the entire world hates them for it.
Subverted for Silk, who is probably the only Spider-Hero other than the aforementioned alternate universe Spider-Girl to be liked by J. Jonah Jameson from the start. JJJ is a fan of Cindy Moon's alter ego and also acts as a bit of a Parental Substitute for her. Which makes things interesting once Cindy starts working as the The Mole and tries to actively ruin her reputation and be labeled a menace to strengthen the facade. Instead, Jonah begins coming up with a number of excuses for her villainous behavior, refusing to believe Silk has actually gone bad. Later on, Cindy ends up devastated when an actually evil version of her from Spider-Gwen's dimension shows up to commit a major crime spree, causing Jameson to finally lose faith in her.
Lampshaded in Sam Raimi's the first movie, where, after Spider-Man rescues numerous people from a burning building, several cops arrive and try to arrest him, in spite of him pointing out he had been rescuing people. Then a person inside the building starts screaming, and one of the officers demands Spider-Man rescue the woman and then come back down to be arrested.
