This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Amazing World of Gumball
Darwin in "The Third", realizing he's almost lost his best friend by being too focused on Tobias.
Rocky in "The Pressure":
Gumball: You've had girlfriends before, right? Rocky: Oh yeah, thousands of 'em. Gumball: Well how do you get rid of them? Rocky: Well usually I just close my eyes, and open my heart! And when I open my eyes again, they're gone...
Gumball and Darwin's song in "The Gi" is surprisingly heartwrenching.
Gumball starts crying near the end of the episode, realizing that everyone has been making fun of him the whole time.
In "The Kiss":
Gumball:THERE IS NO HAPPY PLACE!
In "The Party" when Rachel is crying outside because NONE of her friends showed up. Which can be atributed from they not wanting to go to a "kids" party, to her not actually having friends.
"The Robot" has Gumball trying to sleep in his backyard and crying after Bobert, who assumes his identity, has won over his family.
Rocky talking to Miss Simian in "The Ape":
Rocky: Seriously though, no one likes you Miss Simian, not even me! And I like everybody!
When Gumball runs to his room after being ignored by his parents.
Penny: Well... *sniff* T-thanks for being honest with me....
"The Helmet" has a Disney Death of Gumball when he attempted to get his helmet that was about to fall into the "dumpster's crusher". It made Anais scream at the top of her lungs.
Similarly, though the circumstances were funny, Gumball's reaction to Darwin's Disney Death in "The Phone" is fairly sad - he drops to his knees and starts sobbing.
Teri's (almost) death in "The Virus" is a combination of this and Nightmare Fuel. What's especially saddening is the characters' (Gumball and Darwin) completely heartbroken reactions. It makes it sadder that she's a pretty friendly and sympathetic character, and almost dying in such an horrible way (being decapitated) is quite uncomfortable, even for a kids' show.
The fight scene from "The Words" where Gumball hurts the feelings of Darwin in one of the saddest moments in the show.
Gumball:You are not my brother! You are just a pet, who grew legs!
The two make up but it's still extremely saddening to see. It reduces the two to tears and it's sad to see two friends who stick by each other through so much cry together.
Gumball thinking he murdered Idaho in "The Bumpkin" and crying over it once Idaho's family buries him.
Richard's song in "The Hero".
When Gumball thinks Richard has fallen to his death.
Gumball:He's gone... and I was laughing at him. Why didn't I tell him in spite of everything I was proud, Darwin. I was proud of him! If he were still here I would tell him, if he were still here-*Gumball notices Richard is right behind him* oh, you're here.
In "The Pony", Anais wants to spend time watching a movie with her brothers, but a series of events continually delays Gumball and Darwin from returning home from the DVD store. Anais is at first unamused, no doubt thinking that they've messed up somehow, as per usual, but she eventually begins to consider that they just genuinely don't want to hang out with her and it drives her to tears. She clearly loves her brothers, so seeing her crying because she thinks they don't care about her is heartbreaking.
"The Voice" sheds some light on William. Poor guy, all he wanted to do was hang out with Gumball and Darwin.
Near the ending of "The Kids", where Gumball and Darwin sing, opera style, about how they are growing up. They get better in the end... though they're not sure if that's better or worse.
Maybe it's for the better
No one wants to stay a child forever
Remember the wonderful times we've had
Those happy thoughts now make me sad
They say it's a fad
It's just a new start,
So why do I have this pain in my heart?
Our childhood memories are getting hazy...
Even sadder when you realize that the voices that gave Gumball and Darwin life for almost two seasons were finally sending their farewells due of their voices being broke and needed to be recasted.
Though Sarah exhibited eccentric and creepy behaviors in "The Fan", she really just wanted to fit in, and after being chased down the hallway by Gumball and Darwin, she explains that she feels lonely, but Gumball tells her to leave them alone, causing her to walk away, crying.
Darwin trying to exile himself in "The Allergy".
Penny freaking out and running away in "The Shell", despite Gumball trying to tell her that he likes her true form. Her dad's reaction doesn't help much as he didn't even bother to tone down his comments to the point of calling her own daughter a monster despite Gumball's best effort to calm Penny down. It's satisfying that Gumball delivered a Calling the Old Man Out speech at him in behalf of Penny.
Penny's reaction to her father also did not help make this scene better.
Penny: Gumball! Please tell my father that the monster is going to live in the forest, with all the other beasts! (flies away)
Gumball's risking himself to protect Penny from harm's way even if it means having to break her heart by telling her she's nothing to him... just to prevent her from being hit by a truck by getting her small enough for them to duck under it. Seeing Penny's small form in Gumball's paws after being called nothing to him is saddening to see, even more so that Gumball only did it just to protect her as you can see from his injuries. She eventually knew but that doesn't make it less saddening. As if her father calling her a monster wasn't enough...
Even earlier after Gumball was kicked out by Patrick when he found out what happened and got Penny grounded as well when she wants to break out of her shell, Gumball didn't have dinner and goes to his bedroom depressed while Nicole is very concerned about him not eating because of it. When Gumball says he's fine, he's then ends up crying in his pillow as he thought he won't see Penny again because he accidentally cracked her shell. To see Gumball defeated like that shows how much he loves her and that he may not see her again because he can't convey his feelings to Penny very well that he ended up headbutting her when he was presented the chance. Thankfully it all paid off in the end for him and Penny when she arrived.
As one could see in "The Burden" and "The Bros", Darwin experiences jealousy for the first time and his fears that Gumball's attention went into Penny instead of him. Ho Yay or not, being a goldfish who grew up legs and still naive to the world, Darwin might not know how to deal with such feelings of abandonment and jealousy.
In "The Man", Richard reveals about his father that the last time he saw him was that he went out for milk 42 years ago. Richard thought he would come back eventually and even all these years, but even his family and kids knows that's not the case. In the end, he finally knows the truth and he let his tears out while Jojo comforted him. He actually grew up without a father which explains why Granny Jojo was so overprotective of him, as seen in "The Authority."
And if their ages are to be put into consideration, it's heavily implied that Granny Jojo gave birth with Richard when she's very young. And she didn't know what to do and thus went into extremes into protecting Richard.
The reason why Chris Morris helps Gumball and Darwin avoid getting caught by the police in "The Burden" he doesn't want anyone to experience being caged.
"The Butterfly": The Alligator Woman telling Rocky that she's been saving herself for marriage for so long that she became depressed, couldn't find a job, had to live in a van under the freeway with her cats, and ate noting but squirrels and rust.
"The Friend": The shark-headed monster was left alone to wander the streets in search of friends after his creator died (or, in his words, "didn't wake up") and Gumball, Darwin, and Anais trying to protect him from the police, only for the shark-headed monster to kill himself with cola and mints (Fortunately, he gets better, but still has to leave town because of what happened).
The revelation that Anais has no friends and she threw a birthday party just so someone — anyone — could come. Her sadness on the second season's "The Pony" is justified after all.
Rob telling Gumball and Darwin to forget about him like everyone else has in "The Nemesis". Looks like being in the void really did a number on him.
In "The Signature", Frankie Watterson come back just to betray them and take the ownership of the family's home for himself until Richard looked at him with a very sad look. Frankie then remembered having to look back at young smiling Richard who doesn't know he's actually leaving, waving goodbye at his unknowing son. Seeing this cause Frankie to have a Heel Realization and let his family pass through so Jojo and Louie can get married to claim home ownership back to the family.