In the world of Marvel Comics, Spider-Man is one of the most respected heroes around. His career started at an early age fighting street level, often super-powered criminals. Over the years, he graduated to facing off against the worst supervillains on Earth and beyond. Spider-Man is usually the first to throw himself into the thick of the battle and take on any challenges.
Because of this, he has a long list of friends and allies who are willing to step up to his defense when needed. There are also more than a few heroes who would love nothing better than to never talk to him again.
DESPISE HIM: Storm
In this case, "despise" might be a strong word but Storm sure doesn't seem to like the Wall-Crawler very much. Their paths have crossed on numerous occasions, especially when Spider-Man was helping to educate the young mutants at the Jean Grey School for Higher Learning. Both he and Storm are heroes but they have different ways of approaching the situations they are confronted with. Storm is a serious person while Spider-Man consistently tries to diffuse the situation with levity. Like many people, she finds him quite annoying.
RESPECT HIM: Wolverine
The relationship between Wolverine and Spider-Man took a long time to get somewhere positive but it did get there. Some might find it surprising that they call each other friend, but they do. Tolerance turned into being allies which eventually became a friendship. They stood beside each other in battle so many times it was almost inevitable.
When Wolverine died, his will included a request to Spider-Man that led him to teach at the Jean Grey School for Higher Learning. It was in part to investigate a traitor amongst the students, but he still trusted Spider-Man with the task.
DESPISE HIM: Elektra
Elektra is possibly the most proficient hand to hand combat specialist in Marvel Comics. Despite not having any powers to speak of, she has proven to be more than a match for people that should have been able to easily crush her. Thanks to her finely honed skills and tight, regimented lifestyle, she can dominate almost any fight. Spider-Man is the exact opposite. He is a self-taught, often sloppy fighter who lacks any semblance of discipline. In many ways, Spider-Man is the antithesis of Elektra, which is probably why she doesn't like him.
RESPECT HIM: Daredevil
In many aspects of their lives, Daredevil and Spider-Man are respectively the only people they can trust. Being two heroes working the streets of New York gives them a perspective on their line of work that the likes of Thor and Iron Man simply do not understand.
Each hero uses the other as a sounding board both for hero-related issues as well as personal ones in their secret identity lives. Daredevil and Spider-Man have developed a mutual respect and friendship over the years that got them through some dark times.
DESPISE HIM: Red Hulk
General Thaddeus "Thunderbolt" Ross spent decades of his life chasing the Hulk, in part to stop the monster and in part to use him to create weapons. Thunderbolt's obsession grew so all-consuming that he became a new version of the Hulk called the Red Hulk to fight the classic green one. Maybe it's his military background clashing with Peter Parker's background in science but he doesn't like Spider-Man. On the rare occasions the two men have been forced to work together, things have not gone well.
RESPECT HIM: Mile Morales
It takes a Spider-Man to know a Spider-Man. No one knows Peter Parker quite like Miles Morales does, in part because they share a very similar double life. Originally from the Ultimate Marvel Universe, Morales made his way to the regular continuity after the events of Secret Wars and Battleworld.
Peter Parker has been an influential figure in Morales' life, inspiring him to become Spider-Man once he received his powers. But in the 616 universe, Parker is significantly older than Morales so he took more of a mentorship role in the young man's career.
DESPISE HIM: Cyclops
Calling Cyclops boring might be the understatement of the decade. Even when he's a bad guy who is betraying everything he used to believe in, he's still about as exciting as a sack full of flour. It's not even that he's serious like Storm. He's just a tedious guy to be around for long periods. While Cyclops might not be the most charismatic guy, he is still a leader, a job he does with a high level of professionalism. Spider-Man drives him nuts, not just because he's constantly making jokes but because he might be a better leader than Cyclops.
RESPECT HIM: Human Torch
The Fantastic Four were some of the first heroes Spider-Man met after getting his powers. He broke into their home base to impress them, besting some of their top defenses. It was from that ridiculous act that his bond with Johnny Storm started.
At first, the Human Torch wasn't particularly interested in the Wall-Crawler. Then again, Spider-Man had little or no interest in him. Today, their friendship is incredibly strong, with each man being the first to the other's side in their respective times of need.
DESPISE HIM: Punisher
Frank Castle genuinely despises Spider-Man and you can be guaranteed the feeling is more than mutual. Spider-Man always looks for the best in everyone around him but he wrote the Punisher off years ago. Castle also has little use for Spider-Man. He is a man of absolutes, particularly in his war on crime. Frank sees Spider-Man as weak, wasting his incredible powers which could be used to brutally take down criminals. In Punisher, Spider-Man sees another villain that needs to be locked away. In Spider-Man, Castle just sees something slowing him down, if not another target.
RESPECT HIM: Deadpool
Wade Wilson is the only hero in the Marvel Universe who talks more in a fight than Spider-Man does. Keeping in mind that Deadpool is legitimately off his rocker, the two make a ludicrously good duo. As much as Deadpool respects Spider-Man, he may be full-on in love with the guy. The only hero Deadpool might like more is Wolverine, though that's more for his bloodlust and super cool hair. Simply put, Spider-Man is one of the guys who inspires Deadpool to be a better person and maybe even a hero.