The full story
Spider-Man 2 finds Peter Parker crumbling under the weight of his double life. Two years after becoming Spider-Man, he's failing college, can't hold a pizza delivery job, and has pushed Mary Jane away so completely that she's engaged to astronaut John Jameson. Harry Osborn, now running Oscorp, still blames Spider-Man for his father's death and is funding a fusion energy project led by Dr. Otto Octavius.
Octavius is a brilliant, warm scientist who becomes Peter's mentor. To control his experimental fusion reactor, he fuses four AI-controlled mechanical arms to his spine, with a neural inhibitor chip preventing the arms' artificial intelligence from influencing his mind. The demonstration goes catastrophically wrong—the reactor destabilizes, the inhibitor chip is destroyed, and his wife Rosalie is killed by flying debris. The arms' AI begins corrupting Octavius's mind, driving him to rebuild the reactor at any cost. He becomes "Doc Ock," robbing banks and terrorizing the city to fund his obsession.
The weight of Peter's guilt, stress, and self-doubt causes his powers to fail psychosomatically. He cannot climb walls. His webs won't fire. His vision blurs. In a pivotal sequence, Peter decides to quit. He throws his suit in a trash can—a direct homage to the famous "Spider-Man No More" comic storyline—and tries to live a normal life.
For a while, it works. His grades improve. He reconnects with people. But crime surges without Spider-Man, and Doc Ock kidnaps Aunt May, then later Mary Jane, to lure Peter out. Peter recommits to heroism, and his powers return in full.
The film's greatest sequence is the train fight: Doc Ock rips the brakes off a speeding elevated train, and Spider-Man must stop it with his body, webs, and sheer will. He succeeds but collapses, his mask torn off. The passengers see his face—he's just a kid—and vow to protect his identity.
In the climax, Peter appeals to the real Otto Octavius buried beneath the arms' influence. Otto briefly regains control, recognizes the horror of what he's built, and drowns himself along with the reactor in the East River. "I will not die a monster."
Harry, consumed by rage, discovers his father's Green Goblin lair hidden behind a mirror—the weapons, the glider, the mask—and realizes Norman Osborn was the Goblin.
Mary Jane, now knowing Peter is Spider-Man, leaves John Jameson at the altar and comes to Peter. She accepts the danger. The film ends with her watching, worried but resolute, as Peter swings away to answer a siren.