Eddy walking cold and alone in the Christmas Special, which leads to a Crowning Moment of Heartwarming as he walks up to a Christmas tree, notices a shorted-out light and replaces it with a light he's been holding the whole show, which causes the tree to shine like never before.
"All I want is a good Christmas."
May Kanker sobbing by herself in the closet because nobody got her any Valentine's Day cards, despite normally being the unflappable Ditz.
Her sisters teasing her about the card she wanted to give to Ed, too.
"A Fistful of Ed". Edd being sad because everyone believes him to be a bully. There's also the scene where Ed tells him that they can't be friends anymore and they both start crying. You even see Ed's heart literally break in that scene.
The scene where Edd cries to himself alone in the science room. And after that, the scene where Jimmy witnesses Edd nurse a flower and makes it bloom, proving to him that he's not the monster he's being made out to be.
"Take This Ed and Shove It" Had a bit of a depressing one where the Old Eddy starts breaking down after realizing he really is old and will never be a kid again, beating himself senseless with a Cane and then supposedly waking up as a kid and had only passed out when they were trying to get the jawbreakers, only to wake up again as an old man again and coming to terms that they are all old and he was only reliving his memories in his sleep. And this was going to be the original ending to the series before it came back.
"A Case of Ed". The scene where Edd is giving away his stuff because he thought he was dying.
Heck the whole episode was sad, the nicest character on the show thought he was DYING. The fact that he trusted his friends only to find out they were joking is just insulting.
In "Your Ed Only", when Sarah tearfully said, "I want my diary!" anybody would be upset over loosing something so personal.
It's very upsetting when Jimmy's belief in fairy tales and magical creatures gets crushed in "Tinker Ed". There's a particularly heartwrenching scene where Jimmy, in denial, tearfully reads a picture book about fairy tales in the library, constantly telling himself that they do exist.
There's an episode where the Eds introduce Jimmy to a happy park called "Smiley Ville" (they even produce a map for him) in order to cheer him up. It apparently works, and Jimmy happily enters through the Smiley Ville gates, excited to take part in all the fun things the park has to offer (such as a teddy bear picnic). Upon entering, however, he discovers that Smileyville is no more than a dirty, disgusting alley. Fortunately, Rolf steps in to console the crying Jimmy and get back at Eddy for crushing his hopes.