Pooper: (Thanks Herbmeistr):
The Lizard makes an aerosolized version of the genetic mutation formula and infects several police officers with it. Peter figures out that The Lizard plans to launch the aerosol formula through Oscorp's vapor machine, which would shower it over all of Manhattan, infecting all citizens. Gwen initiates an emergency evacuation of Oscorp so that she can develop an antidote to be launched instead.
Captain Stacy and the police manage to incapacitate Spider-Man temporarily. When he comes to, Peter reveals his identity to Capt. Stacy, who then decides to help Gwen and Peter load the genetic antidote into the Oscorp vapor machine.
On the roof, Capt. Stacy and Spider-Man confront the Lizard. Capt. Stacy briefly subdues him with liquid nitrogen while Spider-Man makes his way to the machine to load the antidote. The Lizard stabs Capt. Stacy with his claws and goes after Spider-Man. Spider-Man loads the antidote just as the machine launches the device. As the antidote rains over New York, the tower on top of the building topples over. Spider-Man almost falls to his death but is caught by The Lizard, who is quickly transforming back into Dr. Conners.
Capt. Stacy tells Peter that he will make enemies, and to only promise that he keep his daughter Gwen out of it. He then dies from his wound.
Peter returns home to Aunt May, and indicates to Gwen that they will continue to see each other when he is not Spider-Man.
Long Version: (Thanks Evan):
The film starts with a young Peter Parker (when a teenager, played by Andrew Garfield) being left with his Aunt May (Sally Field) and Uncle Ben (Martin Sheen) by his parents after unidentified assailants break into the father's home-office, clearly looking for something he doesn't want revealed. The parents, after a tearful farewell, walk out the door never to return.
We flash forward to where Peter Parker (later to become our hero, the Amazing Spider-Man) is a young, high school science geek who, nonetheless, is not afraid to try and stand up to bullies. He still lives with his aunt and uncle, and has clearly inherited the scientific genius of his father. He has a crush on stunningly smart schoolmate, Gwen Stacy (Emma Stone), one of the few people more accomplished than him at school. One night, while helping his Uncle Ben identify an issue with a broken water pump in the house, Peter discovers his father's old satchel. Later that night, he accesses a hidden compartment that contains various papers, including one with a formula scrawled on it. He also determines that his father worked with one-armed scientist Dr. Curt Connors (Rhys Ifans) at Oscorp. The pair studied inter-species cross-genetics.
Peter manages to sneak into Oscorp with a group of interns and discovers that Connors is working on a project to combine human and lizard DNA so that humans can enjoy the regenerative processes that lizards have (i.e. when their tails come off, they can grow new ones). Peter sneaks off into a room containing many dozens of spiders (his father had focused on work with spiders when Peter was a kid) and is, fatefully, bitten by one of them. On his way home, Peter continues to accidentally stick to things and inadvertently displays super-human strength. We also learn that Dr. Connors' experiments are too unstable thanks to a missing formula, and that he and fellow Oscorp employee Irrfan Kahn (Rajit Ratha) played some sort of role in the Parkers' disappearance.
Peter quickly determines that he has gained super-human spider powers, and uses them to exact comical revenge on the school bully. He also personally visits Dr. Connors and gives him the formula he found from his father, thus seemingly stabilizing Connors' own cross-species formula. He also awkwardly asks Gwen on a date. Peter begins becoming cocky and careless, and when Uncle Ben gives him a speech about responsibility that he had learned from Peter's dad, Peter storms out of the house angrily after yelling that his dad was irresponsible for abandoning him as a child. Uncle Ben runs after young Peter. Meanwhile, Peter refuses to stop a thief with a tattoo on his wrist who steals cash from a convenience store, and the thief later encounters and murders Uncle Ben.
Peter goes on a mission of vengeance (and strains his relationship with Aunt May, while remaining undependable), attacking and delivering to the police various robbers who fit the description of the store thief, but none bear the tattoo (in fact, Spidey never does find the thief). Eventually, Peter builds mechanical "web-shooters" and designs his Spider-Man suit. He is invited over to Gwen's house for dinner where he gets into an argument with her father George Stacy (Denis Leary), the police captain of NYC. Captain Stacy notes that Spider-Man is not a hero as he only attacks criminals who share the same physical characteristics (forcing Parker to realize he is using his powers selfishly), is interfering in police investigations by preemptively nabbing villains, and is working outside the law. Later that night, Peter reveals to Gwen that he is Spider-Man and the two share a passionate first kiss, with her admitting she thinks Spidey is a force of good.
Meanwhile, Connors' formula is a seeming success, regenerating mice with missing limbs. It is revealed that the founder of Oscorp, Norman Osborn, is dying and needs the formula to regenerate. Kahn insists they move onto human testing, but Connors refuses and is fired (and Kahn takes the formula, threatening to inject it secretly into wounded war vets). Depressed, Connors looks at his arm stump and injects himself with the formula. He wakes up to find a new arm has grown, but the formula proves to be unstable despite the use of Peter's dad's formula. Connors soon morphs into a giant Lizard (huge tail and claws, is about seven feet tall, and insanely strong) and races off after Kahn's car.
Lizard and Spider-Man (in his first selflessly heroic act) fight on the bridge, with Spidey saving Kahn's life. Spider-Man then saves a child who was trapped in a car that the Lizard had tossed off the bridge. The Lizard flees before the police show up, and Spider-Man is blamed for the damage. Peter knows, however, that he is the only one who can stop the Lizard. He visits Connors in the lab and discovers he is the Lizard when he notices that the test-mice have also developed carnivorous reptilian qualities. Spidey and the Lizard fight several more times (with Lizard discovering that Peter is behind the mask), with Peter being brutally beaten during most conflicts. Though his bond with Gwen grows stronger, her father distrusts Spider-Man more than ever. Meanwhile, the Lizard decides to "improve" humanity by turning them all into lizard-type people by disbursing the lizard-serum in gas form using a powerful machine atop Oscorp tower.
The two super-beings fight in the streets, with the Lizard defeating and/or morphing the cops into lizards. The police go after Spider-Man just as hard, eventually capturing him. Captain Stacy unmasks our hero and discovers that it is Peter, who pleads with him to be freed so he can save Gwen who is at Oscorp tower (where the Lizard is heading). Gwen is using her genius to develop an antidote to the Lizard formula. Captain Stacy lets Spider-Man go, although it is shown that he has been wounded by his struggle with the police. Gwen does everything she can to stop the Lizard from reaching the machine atop Oscorp tower, but is unsuccessful and he activates the machine. With the assist of the people of NYC (led by the father of the child Spidey saved on the bridge), Spider-Man reaches the tower and confronts the Lizard. The Lizard bests him (and breaks his web-shooters), when Captain Stacy appears and helps freeze the Lizard using liquid nitrogen. He gives Spider-Man the antidote Gwen developed and tells him to save the city while he holds off the quickly thawing Lizard. Captain Stacy is mortally wounded, but holds off the Lizard while Spider-Man successfully switches the Lizard serum for the antidote, which the Oscorp machine disburses throughout the city, restoring all infected humans. Spider-Man plummets off Oscorp tower, but is rescued by Connors, whose humanity has been restored. It is too late for Captain Stacy though, who endorses Spider-Man's mission but makes Peter promise to leave Gwen out of his life.
Peter returns home and has an emotional reunion with Aunt May, and it is implied she knows of (and accepts) his double life. Peter attends Captain Stacy's funeral from afar, and when Gwen confronts him, he pushes her away (though she concludes that her father made him promise to leave her alone). Ultimately though, Peter confesses to Gwen that his promise to her father is one he cannot keep, and she smiles. We then see the typical "hero" ending, with Spidey web-slinging his way through the streets of NYC.
We see Connors being escorted to a dark jail cell (and also notice that he still seems to be suffering some effects of the lizard-serum). He appears to be alone, but a figure stands in the shadows of the cell (and we are literally, never told nor explained who the figure is). The figure asks Connors how much Peter knows about his parents, and Connors' silence confirms to the figure that Peter knows very little. The figure is pleased by the info and begins leaving the cell, while Connors pleads with him (likely in vain) to leave Peter alone.
Thanks Herb and Evan!