Spider-Man himself mutating into a hideous, vicious, terrifying man-spider. The change doesn't happen until the very last minute of the episode, but it's still a horrific scene, with Peter's gloved hands mutating into distorted claws before he starts Hulking Out. The Reveal of the new Man-Spider is like something out of a horror movie, with the Punisher, who had been chasing Peter along effortlessly for most of the episode, suddenly finding himself effortlessly manhandled by a towering arachnoid horror. The Oh Crap! face as he grabs Spiderman's torn, discarded mask and holds it up, realizing what this thing was. And then there's the very last shot of the scene; Man-Spider, lit from behind so he's just a silhoutte, with the only features distinguishable being his huge fangs and six glowing blood-red eyes, leaning down in an Eat the Camera shot...
Man-Spider himself is a pretty horrific concept. A hideous six-armed hulked-out humanoid spider is bad enough, but he's implied to be even stronger than the regular Spidey, he has organic webbing and so can web you from six hands at once, he spitsHollywood Acid, oh, and his human brain is implied to be degenerating. Meaning he may reach a point where he starts treating humans as prey...
And later on, the Vulture, with his youth-draining tech, sucking the youth out of people, lastly Spider-Man... and also absorbing his mutating DNA, causing him to sporadically turn into the Man-Spider himself, but retaining his full intelligence and power of speech, and then later seemingly permanently being trapped as the Man-Spider for the rest of his life. Sure, he brought it on himself, but still. Fortunately for him, he's cured by an off-screen plot device...
There's something subtly disturbing about the storylines involving Hydro-Man — his sheer relentlessness combined with the fact that anything Peter does to him will only stall him for a few minutes is bad enough, but then he dies because Mary-Jane tricks him into spending so long away from water that he evaporates, and Spider-Man just has to say that water is so common that it's possible he'll come back one day, which means a) it's possible that he's still sentient in his evaporated form, b) he might return having learned from that defeat, rendering him genuinely impossible to get rid of. And then he does come back. And it turns out that he and the current Mary-Jane are both clones of the originals, and they both just disintegrate into water.
Spider-Man's reaction to him watching Mary Jane fall into one of the portals, presumably to her death. He's out to kill Green Goblin. It's not black suit Spidey, being controlled and crossing the lines. It's Peter Parker, having watched the woman he loves die, and wanting to kill the man responsible.
Not to mention Mary-Jane's fate herself. She spends the rest of the series falling through a wormhole with no escape. And seeing as obvious weeks and months have passed and it still shows her falling, she obviously cannot die in there.
Though Word of God states that if the series wasn't cancelled, we'd learn that she ended up in Victorian London.
While he may have been significantly toned down, Carnage was still pretty terrifying. In fact, back when he was just known as Cletus Kassady, he was specifically quoted to have done things even the post wouldn't print.
A lot of people remember how over-the-top Spider-Man got after being taken over by the symbiote, but the first part of "The Alien Costume" shows how scary a downplayed symbiote!Spider-Man could be.
Rhino: All right, I give up. I'd rather go to jail than to be a snitch. Spider-Man: Who said anything about jail? Rhino: Huh? I-I don't get it. Spider-Man: You will. (shoots a webline at a metal door and reels it in) It's like this, I'm through with not getting what I want! Rhino:What are you doin'? I told ya, I give up! Spider-Man: That's funny. I give up, too. (lifts the metal door above Rhino) I give up trying to be a friendly neighborhood Spider-Man.
Alternative Title(s):Spider-Man The Animated Series