Dork Knight: Though he seems a lot less dorky as Spider-Man than as Peter Parker.
Genius Bruiser: He is top student in science for high school. In college, he can't do anything much in the first half of second film. For second half of second film and entire third film, it's clearly shown he is Dr. Connors' top student.
The Hero: Obviously, he is the main hero of the story.
The Paragon: Best summed up by Aunt May in Spider-Man 2:
May: Too few characters out there, flying around like that, saving old girls like me. And Lord knows, kids like Henry need a hero. Courageous, self-sacrificing people. Setting examples for all of us. Everybody loves a hero. People line up for them, cheer them, scream their names. And years later, they'll tell how they stood in the rain for hours just to get a glimpse of the one who taught them how to hold on a second longer. I believe there's a hero in all of us, that keeps us honest, gives us strength, makes us noble, and finally allows us to die with pride, even though sometimes we have to be steady, and give up the thing we want the most. Even our dreams.
Wall Crawl: Thanks to small hairs on his fingertips.
You Fight Like a Cow: Throws battle taunts once or twice in each film, in other words significantly less than in the comics.
However, this is somewhat justified by the fact that Spidey is known to shut up when things get serious, which is a large amount of both the second and third film. It can also be argued that this was done to keep the tension of situations rather than lose it when Spidey makes a joke, which is one of the most nebulous complaints of The Amazing Spider-Man franchise.
Big Bra to Fill: Mary Jane is one of the curviest non-superheroic females in the entire Marvel universe. Kirsten Dunst doesn't quite have the body Mary Jane in the comics does (but few real life people do).
Maybe not quite, but anyone who saw that scene in the rain knows Dunst is far from flat-chested. She's closer to her character's comic book proportions than just about any other Hollywood actress would be.
Composite Character: She has some traces of Gwen Stacy, flat-out stated by Word of God to be the case. Her lively but pained character is based on comics MJ, but her "girl next door" exterior is comics Gwen.
Mary Jane also has a strong basis in Liz Allan. Like Allan, MJ in the movies is a classmate and longtime crush of Peter's who is much higher on the social latter and dates Flash Thompson (although MJ did briefly date Flash as well, it didn't last long). The actual similarities MJ has with her comics counterpart are her red hair, her being Peter's neighbor, her coming from an abusive household, her brief relationship with Harry Osborn, her vivaciousness in her school days masking her insecurity and pain, and her aspirations to be an actress.
Damsel out of Distress: While she does ultimately have to be saved from falling by Peter (with aid from Harry), she actually gets out of danger repeatedly during the climax of Spider-Man 3 (dodging falling bricks, jumping out of a falling truck, swinging on a web to avoid said truck crushing her and hanging on for a good while), and even saves Peter from Venom at one point by dropping a cement brick on his head.
Adaptational Heroism: The Green Goblin is less sympathetic, but gets a dying moment of decency that would be utterly foreign to the comic-book version of Norman Osborn. Though at the very least prior to being the Green Goblin Norman was shown to be a good man if a bit of an aloof father and stressed businessman, the Goblin formula drove him insane and created a split personality. In the comics as Peter pointed out "He was a bad man turned worse".
Anti-Villain: Woobie Anti-Villain. A genuinely good man and husband wishing to use his intelligence for the good of mankind who turns into a monster because of his failed experiment and tries to replicate it despite endangering half of New York.
Big Bad: He is the main antagonist of the second film, though his metal arms are actually manipulating him.
Combat Tentacles: Well he is called Dr. Octopus. And the four metal arms look like tentacles.
Peter's photographer rival, who later bonds with an alien symbiote Peter gets rid of.
Adaptational Villainy: Comic book Venom had some traits of being an anti-hero, he would try to protect innocents and stop other criminals when not seeking Spider-Man. Here, Eddie fully admits to Peter that he enjoys being a villain. Even before the merge, Eddie was a self-centered jerk who felt the world was centered around him.
Big Bad: The Venom symbiote is this in the third film, with Brock/Venom as the Final Boss.
Composite Character: This version of Eddie is a mixture of the mainstream and Ultimate Venoms, with a touch of the animated series thrown in for good measure. This version even has some elements of Venom's offspring, Carnage, such as having bonded with the symbiote so completely that he refers to himself with singular pronouns rather than the plural pronouns that comic Venom does and being a completely psychotic villain with no redeeming qualities as opposed to comic Venom who, outside of his innate hatred of Spider-Man, is a classic Noble Demon style Anti-Villain.
Evil Counterpart: To Peter. He is a reporter like him, but tries to earn his money through framing rather than decent work. He tries to get a girl, but through imposing himself on her. He gets Spider-Man esque powers, but choses to become a villain rather than a hero etc etc
Fangs Are Evil: After bonding to the symbiote he has fangs even with his mask retracted.
Freudian Excuse: Averted. All the bad things that happened to him are completely his own fault and deserved and him becoming a supervillain rather than making up for his faults shows just how much of a self-centered jerk he is.
From Nobody to Nightmare: Goes from being a disgraced jerk of a photographer to a legitimate threat to Spider-Man simply by virtue of being in the right place at the right time.
It's All About Me: His purpose in the film is to show someone (unlike Peter, MJ, and Harry) whose descent into selfish behavior is irreversible and who can't forgive others for their selfishness toward him.
More Teeth than the Osmond Family: Eddie has the classic gaping maw full of fangs, but unlike most other versions the symbiote's mask acts as lips so they're not visible when his mouth is closed.
Never My Fault: True to his comic self, he blames Peter/Spider-Man for his shortcomings rather than take responsibility.
Paparazzi: Harasses Spider-Man trying to take pictures of him to win the Bugle's contest, and when Spider-Man smashes his camera out of frustration Eddie photoshops a fake image to incriminate him in a bank robbery.
Tainted Veins: When he retracts his mask, tendrils of the symbiote remain stuck to his face and neck and give him this appearance. In addition, the silvery webbing motif the symbiote manifested when bonded to Spider-Man becomes distorted and vein-like when bonded to Eddie.
Kick the Dog: Yes, he is a tragic character and he wants to help his daughter, but him willingly teaming up with Venom to kill at least a few dozen cops and brutally beating Peter to near death was still not justified.
Mighty Glacier: His speed is greatly reduced while in his "sand giant" mode.
Demoted to Extra: None of characterizations from the comics made it into the trilogy with the exception of being Peter's potential love interest, and even that isn't as prominent compared to the source material.
Sexy Secretary: To the point that both Peter and Eddie hit on her as much as they can in the third film.