The Amazing Spider-Man (1977)

Peter Parker has a laboratory accident that changes his life. He finds himself with greatly increased strength, the ability to stick to walls to climb them without needing hand and footholds and a "spider-sense" (presented in this series as clairvoyance) that allows him to sense danger. Designing a costume and a webshooter that allows him to fire a strong artificial web, he fights crimes as Spider-Man.