Spider-Man adopted an alien costume in Marvel Super-Heroes Secret Wars #8 and Amazing Spider-Man (1st series) #252, wearing it until it was revealed as a symbiote in #258. He hosted the cosmic powers of Captain Universe from Spectacular Spider-Man #158 to Amazing Spider-Man #329, during Acts of Vengeance.
The Clone Saga was a two-year event running through all Spider-Man titles circa Amazing #394-418. In that Saga, Peter Parker temporarily assumed the costume of the Scarlet Spider, was convinced he was the clone while Ben Reilly was the original Spider-Man, lost his powers while exposed to the same radiation that first irradiated the spider that bit him, but finally reclaimed the name, powers, and costume of Spider-Man.
During Identity Crisis, Spider-Man was framed for numerous crimes by Norman Osborn, leading him to assume four separate new identities to operate in public: Hornet, Ricochet, Dusk, and Prodigy. The event lasted two months circa Amazing #434-435.
A man named Ezekiel Sims revealed a second, mystical aspect of Spider-Man's power to him beginning with Amazing Spider-Man (2nd series) #30. This led him through two mutations in Spectacular Spider-Man (3rd series) #17-20 and The Other crossover, circa Amazing #525-528, where he received enhanced powers such as organic webbing, bone stingers, communicating with spiders, etc. These powers mysteriously vanished after his deal with Mephisto restoring his secret identity in Amazing #544-545.
One side effect of the new reality engineered by Mephisto was that a techno-mystical spell crafted in part by Iron Man, Mister Fantastic, and Doctor Strange not only wiped all knowledge or record of his secret identity from the world, it also actively prevented people from re-learning Peter Parker was Spider-Man. The spell became weaker as Spider-Man revealed his identity to several associates like the Fantastic Four and his Avengers teammates. By Amazing #673, the active elements of the spell were gone -- the world would not remember Peter Parker was Spider-Man, but anyone could learn if confronted with evidence.
Beginning with Amazing #648, Parker's work at Horizon Labs led him to improve his Spider-gear, developing specialty suits like Stealth, Armored, or Anti-Sinister Six spider suits. He has also created different kinds of webbing and spider-tracers.
In Amazing #697, Doctor Octopus successfully swapped bodies with Peter Parker, leaving Spider-Man to die in his terminal body in #700. Becoming the Superior Spider-Man, Ock's procedure allowed him full access to a memory template of Parker to support his ruse. This copy of Peter Parker's mind eventually supplanted Octavius and reclaimed his identity in Superior Spider-Man #30-31.