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Tear Jerker: The Spectacular Spider-Man
The look of defeat on Peter's face when the Symbiote asks him to join with them. After having one of his worst memories dug up, he looks like he's crossed the Despair Event Horizon as he starts to accept. Thankfully the memory of his uncle steps in to snap him out of it.
Eddie Brock's final refusal of friendship from Peter.
Venom: WE'RE NOT BROTHERS!!! Our parents may have died together, but you had your precious Aunt and Uncle. We had no one. We've always been alone... until now.
When Peter Parker broke up with Liz Allan, she created a huge scene specifically meant to gain the attention of the crowd, making it look like she was doing the dumping instead. As it turns out, this was actually a way of hiding her pain, because immediately after she "storms off", she is seen hiding behind a corner, crying her eyes out. This version of Liz Allan actually had genuine feelings for Peter. It really shows the strength of the writers when they can pull off emotional scenes even with relatively minor characters from the comics.
The ending of "The Uncertainty Principal". Harry is revealed (falsely) to be the Green Goblin and has been drinking the addictive and unstable Globulin Green. Norman is pissed and demands answers. Harry throws him at a wall and tells him that he only wanted to be the son he wanted. He then keeps switching moods due the prolonged addiction. It was both sad and scary.
And we later find out that said father he was ranting at had just got done setting him up as the Green Goblin, which included twisting his leg. Which makes this scene even sadder in hindsight.
The fate of John Jameson/Colonel Jupiter. Knowing that this is the same person we saw as a normal man who saved a building from the Green Goblin makes it even worse to see him as a crazed psycho.
"I miss the power... I need the power... GIVE ME BACK THE POWER!! GIVE IT BACK!!"
Made even sadder when you realize who's in the cell next to him, and how their situations are VERY similar. And it's one of the few times we see J J showing anything other than anger or smarmy condescension. The look on his face is heartbreaking.
The fate of Mark Allen, aka Molten Man is very similar.
Electro in general was a very emotional character. In his early appearances, he didn't want to be what he was. It was just a cruel twist of fate. His "condition", however, slowly consumed his mind and drove him a little nutty- though that doesn't really make him any less sympathetic.
Harry watching Spider-Man accidentally "killing" the Green Goblin, his father, in the series finale. Peter's expression of guilt and subtle despair reflect his failure despite everything he could do.
Spidey working with Uncle Ben's killer. Every word out of his mouth is rushed and aggressive, giving the sense he's only barely keeping himself from falling apart in the man's presence. Even at the end, when the man chooses to sacrifice his chance at freedom to contain the criminals Peter can't ever bring himself to change his emotions.
"This doesn't change anything... you're not forgiven!"