Warning: SPOILERS for All-Out Avengers #5
Not even the Avengers know Spider-Man's true abilities - which means true terror strikes the team when he turns against them. Peter Parker isn't always an Avenger, often preferring to work as a solo superhero rather than part of a team, but he frequently teams up with Earth's Mightiest Heroes nonetheless. In All-Out Avengers #5, Spider-Man fights every single Avenger during a mind control plot gone wrong - and proves the Avengers don't know Peter's true abilities as much as they thought.
To readers, Spider-Man's powers are quite simple: Peter Parker has super-strength, the ability to climb on walls and has a mysterious "Spider-Sense" that allows him to anticipate nearly any attack. Over the years, Peter acquired new powers, though these were not technically part of his own physiology. The gadgets that Peter carried included a pair of trusty webshooters, an illuminated Spider-Signal, and a utility belt which occasionally carried forensic equipment (similar to Batman), but was eventually used only for spare web cartridges.
In All-Out Avengers #5, written by Derek Landy with art by Gren Land, Spider-Man expertly avoids the Avengers as the team attempts to defeat him and take a scrambler device that is secretly manipulating him. Unknown to the Avengers, it is their minds that are scrambled, and Peter is attempting to reverse-engineer the scrambler to revert their minds to normal. Avoiding Thor, Iron Man and Captain Marvel, Spider-Man loses his shirt but also gives the team the slip. "Can he turn invisible? Like the other one?" asks She-Hulk - inadvertently betraying the fact that the Avengers don't know the powers of their most famous teammate.
Not Even The Avengers Know All of Spider-Man's Powers
To the average civilian (and the Avengers), Spider-Man's powers are a complete mystery. His webbing comes from gadgets he invented, but this is not generally known among the public; the rumor that he creates the fluid from his body is mentioned often, and some even believe Spider-Man to be a mutant because of this. When She-Hulk mentions the "other one", she is referring to Miles Morales, a Spider-Man who can turn invisible and has limited electric-based powers, complicating the rumors surrounding Peter's powers.
This also proves how little Spider-Man shares about himself to his allies. Peter Parker is incredibly guarded when it comes to his secret identity, and this naturally extends to his powers. He has seen firsthand what happens when his identity is public - his loved ones are targeted, captured and even killed. Thus, Spider-Man has every right to hide his powers from the Avengers, and the rumors surrounding the wallcrawler only serve to strike fear in the hearts of criminals who would oppose him.