Spidey's tirade against Madame Web matched what many viewers felt about her.
Spider-Man: I am sick of you... and your riddles. And your lessons! And your SUPREME ARROGANCE! Don't you ever, EVER enter my life again! Do you hear me? DO YOU HEAR ME!?
Though she DID return, after the Mary Jane clone died, to have him participate in the Secret Wars. But it took quite a while before she did. Spidey wasn't happy about seeing her again, still not forgetting he was willing to do anything for her IF she'd help him out when he really needed her to...and she refused, hence the tirade. Needless to say, she was willing to when she returned, though as always Spidey had to be thrown into it kicking and screaming.
Say what you will about most of the bad guys, but Electro shot down the S.H.I.E.L.D. helicarrier. Adaptational Badass, thy name is Max Dillon. But in this version, he's Rheinholt Schmidt, the son of the Red Skull.
How does Spidey stop a madman who's actually an alternate Spider-Man bonded with the Carnage symbiote from destroying all realities? Get an alternate version of Uncle Ben to get through to Spider-Carnage and stop him without even as much as beating the tar out of him.
Before that, the Spider-Man actor jumping in to help, despite having no powers.
Peter was finally able to put his foot down for once and told Anna Watson off when she tried to blame him for what happened to her niece. This scene was very brief but it showed that Peter Parker was in no mood to put up with Anna's attitude.
"Jigsaw" Jameson. That is all.
Mary Jane taking out Hydro Man. Both times.
The Kingpin completely owning Scorpion with the Mega-Slayer:
Kingpin: Gargan, your corrosives have no effect on this robot! Scorpion: Oh yeah? How about this! (Scorpion swings his tail, but the Mega-Slayer grabs it) Kingpin: YOU FIGURE IT OUT! (the Mega-Slayer swings Scorpion around until his tail snaps, sending him flying) Kingpin: I broke him? A pity. I was just starting to have fun!
One of the last (but not the last, unfortunately) scenes in the whole series is Spidey, visiting a dimension where he is just a fictional character (unsubtly suggested to be our universe), carrying Stan Lee under one arm, giving him a webline tour of New York.
A more meta example is how the show was infamously prone to some heavyExecutive Meddling which banned punching, saying anything like die, kill, or murder, regular guns and weapons, and breaking windows. And yet, the creators were still able to make a great show even with those restrictions set in stone. Hell, a lot of people didn't even notice the fact that Spider-Man never punched people before they were told, in fact some people still don't notice it.
The Alien Costume part 3 is a crowner for giving us a harrowing chase between Spider-Man and Venom. While still a kids show, it was a particularly tense episode.
Debra tackling a Lizard Folk man and knocking him down.
The Kingpin's final scene in the series. Despite having been the main non-powered villain in the series for quite a while, he managed to put quite a final stand against opponents much more dangerous than he was (namely, a certain Red Skull), all while helping Spider-Man. Even he was respectful of the Kingpin as he was led to jail, and this was treated as quite the important moment.