The Cameo: Stan Lee and Bruce Campbell, in all movies. Stan Lee protects a little girl in the havoc created by the Green Goblin in the first film. In the second, he pulls a woman out of the way of falling debris while Spider-Man fights Doc Ock; "Look out!" is his only line. In the third, he has a much more substantial cameo as a man who talks to Peter on the street. "Y'know, I guess it's true what they say: one person really can make a difference. 'Nuff said."
Bruce Campbell appears once in every film as someone who actually helps develop Peter's plot in some small way. In the first movie, he plays the ring announcer who introduces Peter as Spider-Man instead of "The Human Spider" as Peter originally wanted. In #2, he plays an usher at the theater who refuses to let Peter in because the doors have already been closed. Finally in #3, he is a french Maître d' at a restaurant who gladly helps Peter with his plans to propose to Mary Jane (though it doesn't exactly work out).
In the licensed games based on the films, Bruce also serves as the Lemony Narrator who walks you through tutorials. Though he doesn't seem very interested in it; at one point, he leaves to grab a sandwich.
The Coconut Effect: The movies start off highlighting Spidey's use of Spider-Sense in slow-motion, but as the films progress, the Spider-Sense is more often implied that explicitly depicted, usually in the form of whiplash-quick reflexes and/or Off Hand Backhands. Notably, the third movie never highlighted it at all, with Spider-Man's reflexes and Spider-Sense all rendered in real-time.
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). In fact the only real similarities MJ has with her comics counterpart are her being Peter's neighbor, her coming from an abusive household, her brief relationship with Harry Osborn, and her aspirations to be an actress.
All of whom have died in the comics, they just ended up coming back afterward.
To be fair, how many major comic book characters haven't died at some point or another?
Death by Secret Identity: Green Goblin is impaled soon after he discovers Peter's secret. In the second film, a big part of the movie marketing was that Harry would learn Peter's secret, but Harry's death wouldn't come until he made the full transition to baddie in the third movie. Peter also reveals his identity to Doc Ock, probably knowing that this trope would spell death for the doctor. In the final movie, this works against Eddie Brock/Venom, but actually leads to the redemption of the Sandman. If this trope is truly in full swing, then all those people on the subway in S2 better look both ways before crossing the street...
Development Gag: The second film has a couple of playful jabs at Tobey Maguire's back problems, which nearly forced him to drop out. This includes the "I'm back, I'm back! ...My back, my back!" scene, and a Freeze Frame Bonus Bugle headline claiming link between back pain and brain shrinkage.
Eddie Brock after bonding with the Venom symbiote.
"Ooh, my Spider Sense is tingling, if you get what I talking about. Tiger."
Female Gaze: Well, of course. We're talking about a muscular young dude who wears a skintight outfit and is unbelievable agile.
Foreshadowing: In the first film Harry Osborn says of his father "If I'm lucky I'll be half the man he was". Come the third movie, we find out what exactly is meant by this. There are other foreshadowing moments involving Harry, such as the green bowtie he wears during the wedding scene in 2, and "They're my best friends ... I'd give my life for them".
The novelization looks deeper into his motives: Jameson always protects his sources, and has gone to jail twice for doing so in the past.
In the third movie, he's furious that Eddie Brock gave him fake photographs of Spiderman, commenting that "We haven't printed a retraction in twenty years!" Not only did he fire Brock, but additionally had him shamed on the front page alongside the retraction.
Large Ham: All the villains but Sandman. Also, J. Jonah Jameson and Bruce Campbell's cameo appearances.
Special mention has to go to Willem Dafoe as the Green Goblin. When he is fighting Peter, he is having the time of his life, complete with evil cackles and poor one-liners.
Evil Is Hammy: In addition to the villains, Maguire was having FAR too much fun being Emo-Jerkass-Peter in the middle of the third film.
Made of Iron: Spidey is a given; his powers allow him to shrug off huge amounts of punishment. But especially notable is Ock in the second film. He's an out-of-shape scientist who shouldn't be standing after one of the super-strong Spider-Man's punches. Even if Spidey pulls his punches, Ock takes a web-slung bag of coins to the face at one point without a mark to show for it, and also keeps fighting after being slammed through the floor when Spidey catapults himself from the roof.
Running Gag: Jameson keeps yelling for "HOFFMAN!" who keeps appearing faster and faster as the movies progress, much to Jonah's confusion, eventually culminating in Jameson screaming his name while turning around, only to be face to face with Hoffman before he finished saying his name.
To be fair, in the comics, the web fluid is normally super compressed and expands on contact with the air. As a general rule, a golf ball sized packet of compressed web fluid is enough to fuel all the webbing you need for at least a day, even if used heavily and frequently, and it doesn't weigh much. So Pete doesn't need very much extra mass.
Spontaneous Crowd Formation: In the first film, they help Spidey by throwing insults and rocks at the Green Goblin. The second film plays on this, by having the crowd stand up to Doctor Octopus, only for him to easily brush them aside, snatch the defeated Spidey and carry him off.
Starving Student: Peter Parker, particularly in the second movie which has him struggling through college without money and his superhero identity compounding his hardships.
Trailers Always Spoil: When you watch the trailer after watching the movie, it's impressive how much plot is given.
The most egregious example has to be showing Harry pulling off Peter's mask in the second film.
Tragic Villain: Norman Osborn, before the "Goblin" takes him over completely. He might have been rough and far from a saint but his reaction to finding out he killed people was to be horrified. The way he's been treated seems rather unfair too: A major funder switches their funding to a clearly inferior solution because they personally dislike him and the board of directors fires him from the company he built to get more money.
Doc Ock, a patient teacher and loving husband who inadvertently caused the gruesome death of his wife when his experiment went horribly wrong. After crossing to the dark side for much of the movie, he chooses to sacrifice himself to save the city in the end.