The movie opens with Peter Parker sitting in his day job at the Daily Bugle. He's flicking through the newest release of the eponymous newspaper, passing by an article with a picture of the Runaways before reaching one about an open demonstration of the effects of the newly-discovered gamma radiation on that day. He rushes out and runs through the streets to get there in time, when Flash Thompson trips him over. As such, he's late to the demonstration, being scolded by genetics professor Miles Warren. He suddenly grabs his hand in pain - a spider had bit him.
The next day, in high school, electronics professor Otto Octavius is demonstrating a new invention of his, a set of mechanical arms made to help increase productivity in a workplace. It goes haywire and smashes the whiteboard before turning on Mary Jane Watson. Peter saves her by prying the arms off of her much to everyone's suprise. When Otto questions his strength he puts it down to a rush of adrenaline.
Mary Jane invites him to see her band, The Mary Janes, perform, and he accepts. Gwen Stacy, Mary Jane, Glory Grant, and Carlie Cooper are playing their newest song, 'Face It, Tiger'. He applauds them once it's over and asks Gwen in particular if she'd like to go for food some time. She accepts, and when Peter goes over to his friend Harry, it is pointed out how chuffed he is. They walk to his home together.
Harry's father Norman seems to be frustrated - he snaps at Harry for simply not putting his shoes on the shoe rack. When Peter questions it, Harry explains that his dad has been acting up ever since he started leaving mysteriously. Peter decides to investigate. While doing this, he discovers his wall-crawling powers, and is certain for sure that the spider bite did something to him. He watches Norman chug down a serum, before dropping it and shattering it. His veins begin to protude as he cackles, and Peter retreats.
At Peter's date with Gwen the next day, he's about to tell her about his powers whenever a robber shows up and holds the cashier at gunpoint. They take the money and leave, with Peter doing nothing. Deciding it would be embarrassing to tell her he had power, he holds out and the two run away instead. Later that day, he returns home to see police surrounding his home. Informed that his Uncle Ben has been killed amidst a robber's crime spree, Peter begins to sob and recalls a phrase his uncle coined - with great power comes great responsibility. He adopts a new outfit and the name Spider-Man - from that day on, he'd fight crime and save as much people as possible.
The next day, Spider-Man's first job begins when the criminal Herman Schultz tries to rob a bank. He catches him by making a traditional web in the doorway and watching him run straight into it on his way out. Police Captain George Stacy thanks him for his help, then pulls Herman from the web with Spidey's help and handcuffs him, putting him in the back of the police car. Spidey, alone, realises that that was Gwen's father before swinging away.
When Peter gets to the Daily Bugle, editor-in-chief Robbie Robertson calls him into the boss's office where J. Jonah Jameson demands that Peter bring in pictures of this 'sensational Spider-Man' that attack his status as a hero. When Peter questions it, he's threatened with being fired. As soon as he leaves, he figures out a way to take these photos - by webbing his camera to a wall and setting it to take automatic pictures, he'll be able to fight as Spider-Man. His first use of this set-up is whenever there are reports of terrorised city streets - none other than Otto Octavius.
Peter and Otto fight, under the pseudonyms of Spider-Man and 'Doctor Octopus' respectively. Otto gets the upper hand, pinning Spidey to a wall, who manages to web up his eyes and break free. He narrowly escapes various objects being thrown at him, but is eventually knocked down and grabbed by a tentacle arm. Otto brings him up to a trainline and attempts to pin him down in front of a train, but Spider-Man manages to avoid it and climb on top of the train. The two fight there, Doctor Octopus successfully setting the train off the tracks and forcing Spidey to web it from behind.
While Peter successfully stops the train from crashing, Otto has already escaped. The citizens on the train thank him for saving their lives, but he rushes off before they can properly congratulate him - he needs to get back to work with the camera. When he does, though, J. Jonah Jameson shames him for not catching any of the train fight as it had left the camera's radius at that point. Peter says that he simply couldn't get there in time, but Jonah threatens a cut to his wages and sends him off to try again. On the way out, Gwen stops him, saying that she wanted to talk in private.
When they do, she explains that she loves Peter, and apologises that she never had a chance to say it thanks to the robber at the restaurant. He says that he loves her back and the two kiss, walking away hand-in-hand. Meanwhile, Otto stands in a laboratory at Roxxon Energy Corporation, his new boss Hugh Jones welcoming him to the company and asking if they can do him any favours - to which he replies kill Spider-Man.
During a wrestling match between Bone Saw McGraw (once Crusher Hogan) and the Jersey Devil, Jonah leaves the stadium to answer a phone call from Robbie Robertson. However, the voice that answers is instead that of 'Angar the Screamer', demanding that Spider-Man shows up or he would induce amnesia on all of the staff at the Bugle. Jonah then contacts Peter, telling him that there's a scoop at the Bugle but to be careful.
At the Daily Bugle, Angar is about to scream and give everyone amnesia, but a web hits his mouth in time as Spider-Man shows up. He disperses a few feet away, as the webs drop on the ground drop to his feet, and claims that his work was done, then disappearing completely. A confused Spidey is suddenly hit by one of Ock's tentacles, realising that he's been lured into battle. The two fight again, and this time Spider-Man emerges victorious. He webs Doctor Octopus up for the police, then swings away again.
Meanwhile, Norman Osborn is searching haphazardly through a clipboard, pages flying everywhere. He rips out a page, and the camera pans in to show that it says 'GOBLIN SERUM ANTIDOTE'. When he begins to make it, he has a breakdown and shatters the equipment, ruining the batch and cackling. He tells himself that it's too late to try and cure himself, and that now that he's drunk the serum, he's become The Goblin.
Spider-Man finds himself solving another petty crime, trapping a robber in an abandoned warehouse. He recognises it to be the man who robbed the cafe - and who killed his uncle - and begins to attack him without remorse, bringing him to near unconsciousness. He catches his breath as he realises what he did, carrying him out and leaving him to the police. He doesn't say a word, but leaves in shame that he assaulted the robber so severely.
In the post-credits scene, a man breaks into Norman's lab, stealing the serum notes for himself and running away.