Actor Allusion: When Spider-Man breaks Eddie Brock's (played by Topher Grace) camera for no reason (at least from Eddie's point of view) the latter calls him out with a "What the hell!?" This was a pretty regular reaction by Eric Foreman whenever one of his friends also pulled a seemingly unprovoked dick move.
Deleted Scene: Part of the scene where Peter looks at his reflection while wearing the Black Suit under his clothes was cut that would have shown Peter having a vision of himself as Venom, which explains the alarmed expression on his face and him locking the Black Suit away immediately afterwards. The Venom model that was used harkened back to the character's original appearance, without fangs or distorted eyes.
Executive Meddling: The reason Venom and Gwen are in it (though Eddie Brock was always planned, just not his alter-ego).
Venom and the entire symbiote arc weren't supposed to be in the movie at all. Instead Sandman was supposed to team up with Vulture, who would be his cellmate that vowed revenge against Spidey after being busted by him. Vulture was supposed to be played by Ben Kingsley. Also, rather than being forced to break up by Harry, Peter and MJ would break up naturally after several bad decisions by both. However, studio executives forced Raimi to bring in Venom, a character he was both unfamiliar with and uninterested in, because they thought the character would get more money from audiences. This interference lasted throughout the entire production, leading to several deleted scenes like Harry being talked out of his revenge by Mary Jane rather than his butler, Gwen being kidnapped since Eddie is convinced Peter loves her rather than MJ being kidnapped yet again, Sandman's daughter showing up and talking him out of the final fight, Eddie actually seeing Marko's situation with his daughter rather than knowing it out of nowhere, and others. This meddling is also the reason why a Spider-Man 4 was never made. Raimi and executives just could not agree on a script that would satisfy both parties, so Raimi left.
Kirsten Dunst only agreed to do the 3rd film on the condition that Mary Jane would not end up as the Damsel in Distress. Executives agreed. MJ was originally going to have a more proactive role in the film's climax (Gwen was going to be the damsel while MJ would be the one to talk Harry into helping and forgiving Peter; her lines from this scene remained in the trailer). When the plans changed, they made sure MJ was an Action Survivor during this particular distress as means of making it up to an upset Dunst. Throwing a cinderblock at Venom was thrown in, they let her jump and swing on hanging webs herself before needing to ultimately get saved, and any of MJ's screams during the scene (Peter's too, for that matter) were recycled audio. On the audio commentary, Raimi tells a rough story of coming to the process that in order to finish the movie on time, they had to put MJ in danger, which not only angered himself for reneging on his promise to Dunst before production started that he wouldn't, but that summoning the courage to tell her was one of the hardest things he's ever done in his long time in the business.
What Could Have Been: The Vulture (who would've been played by Ben Kingsley) was originally going to be one of the main villains and would play the Final Boss role that Venom ended up playing. He was ultimately decided against since his role had no meaningful personal connection to the hero at all: he was merely Flint Marko's cellmate who hated Spider-Man for putting him in jail to begin with.
Neither Venom nor Gwen Stacy were present in the original planning packet, with a random woman serving the role Gwen later took.
Also, Gwen was originally going to be kidnapped for the final battle, not Mary Jane; Mary Jane would have talked sense into Harry instead of Harry's butler. A line Mary Jane said for this scene was actually used in the trailer: "We've all done terrible things to each other, but we have to learn to forgive each other or else everything we ever were will have meant nothing."
A scene with Eddie Brock coming to the Stacy's front porch and begging Gwen to take him back was actually filmed but not included in the final version, mainly since it connects with Gwen being the kidnap victim in the end, which was also cut.
An entire character, a doctor whom Marko strongarms into helping find a cure for his daughter, ended up on the cutting room floor, even though he had evidently filmed several scenes. Ouch!
Willem Dafoe filmed several scenes as Harry's hallucination, but in the final movie only has one.
The scene where Marko meets Eddie was quite different from the "90's Batman" villain team-up that was shown. After seeing Flint pretending to be sand in a park's playground for his little girl to play on, Eddie comes up and talks to him, and convinces him that his girl may be cured yet, and he will help him get the cash if Flint helps him take on Spider-Man. Images of this park scene being filmed actually exist. This, followed by him learning from his daughter that she is irrevocably sick and just wants to die with her dad a good man, makes his Heel-Face Turn at the end, and Peter forgiving him, much more credible and poignant.
These scenes most likely were considered, at least somewhere along the line - they were, after all, used in the Peter David novelisation in lieu of what the movie actually gave us. Though the novelisation presents Peter and Flint making amends partway through the battle, while the film shows it after Venom is defeated, and it's really up to the audience to decide which is better (since stopping a big climactic action sequence so that characters to clear things up is pretty hard to pull off in a film). Both exist in some form, at least.
It is also rumored that John Jameson was originally to have an appearance, unknowingly bringing the symbiote back from his astronaut mission like he has in two otheradaptations.