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In the films "Spiderman 2" and "Spiderman 3," Dr. Curt Connors is played by Dylan Baker. Although he's mentioned in the first film, he never appears in it. He's an amputee, but this is never delved into in these films. At first he thinks Peter Parker/Spiderman, one of his students, is brilliant but also lazy. This is, of course, because Dr. Connors doesn't realize Peter has a double life as a superhero. By the third film, Dr. Connors has seemed to develop a soft spot for Peter and advises him not to use any of the foreign Symbiote he's found, although Peter sadly doesn't listen. But in both these two movies, although the two of them possibly get off to a bad start, Dr. Connors never becomes Peter's enemy.
In the movie "The Amazing Spider-Man," Dr. Connors is played this time by Rhys Ifans. He's a geneticist and has a wife named Martha and a son named Billy, although they sadly never appear or are even mentioned in the film. Dr. Connors once worked with Peter Parker/Spider-Man's late father, Richard, and for this reason the two of them are drawn to each other. After being bitten by the spider at OsCorp and receiving his new gifts, Peter introduces himself formally to Dr. Connors, who then instantly recognizes him. Years earlier, when Peter's parents disappeared and subsequently died, Dr. Connors felt so guilty and angry he couldn't bring himself to say anything to Peter or his family, something for which the doctor now apologizes. Dr. Connors continues to pity Peter, who seems to look up to Dr. Connors as a sort of substitute father. It's also due to their mutual love of science and technology that they share this bond. As Dr. Connors lost his right arm years ago, he feels incomplete, much in the same way Peter does over having no knowledge of why his parents left him when he was young. Dr. Connors wants to regrow his lost limb, and, after being given a scientific formula by Peter (which Peter got from his father's research), Dr. Connors uses it to do so - but with unintended side effects: he becomes a human-sized Lizard, and soon he starts wreaking havoc on all New York. Peter, after receiving his own new abilities, inadvertently finds out Dr. Connors' secret identity, and, feeling responsible for this due to his giving the doctor the formula himself, Peter makes it his duty to stop him. By this time, the Lizard knows Peter is Spider-Man, and although the two of them still share their bond and connections with each other, they inevitably become enemies. Peter's girlfriend, Gwen Stacy, another of Dr. Connors' proteges, and her father, police officer Captain George Stacy, both help Spider-Man by administering and giving him a reptilian antidote to use on Dr. Connors. The Lizard, in his reptilian form, kills Captain Stacy, but Spider-Man is able to administer the antidote to the doctor. The now human-again doctor then redeems himself, albeit only somewhat, by saving Peter's life (as he would've fallen from atop a skyscraper), but sadly it's too late to save the Captain. After being returned to his human self and then getting arrested and confined to his asylum cell, Dr. Connors is asked by a mysterious man if he told Peter the truth about his father. Dr. Connors says no, and the man is pleased with this, but Dr. Connors, somewhat aggressively, orders the man to leave Peter alone.
In both his film incarnations (though far more so in the latter), Dr. Connors, though an adversary of Spider-Man's, is, at the same time, a friend and mentor to Peter Parker. Therefore, I can only imagine how difficult it must sometimes be for Peter in his secret life as a superhero.