This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Tiny Toon Adventures
The mother whale being captured in Whale's Tales.
The whole third segment of Cat's Eye View: Homeward Bound. Furrball's cardboard box house falls apart in the rain and he must seek shelter. He befriends a kitten and a rich girl, but the kitten's parents and the girl's parents don't want a filthy cat in the house. Tossed into the streets, he sees a homeless boy who's also not welcome in their house. So Furrball shares his lunch with him. They may not have the best life, but they now have each other.
Furrball and the ribbon in Strung-Along Kitty.
Heck, most Furrball centered episodes tended to be downers, given the poor little guy's miserable lot in life.
The newsclip from Fields of Honey, particularly when Bosko fades away into oblivion.
Babs:(crying) That's the saddest thing I've ever heard.
This is even worse when you realize the same thing will happen to the Tiny Toons, due to them being forgotten over time. Someone actually did a fanfic of this...it was depressing.
Later, when Babs realizes that the old lady she encountered turns out to be Honey, who turns back into her old youthful self when everyone laughs at her cartoons again.
The infamousDowner Ending to "Out of Odor": after spending the whole cartoon being chased by Elmyra, Fifi ends up being caught by her. Naturally, she whips out her tail, hoping her trusty Stinky Skunk status will save her from Elmyra's infamously rough "loving"... except that Elmyra's allergic to roses, specifically the ones from the rose parade float she's driving, so she's immune to Fifi's stench. A happy Elmyra promptly drags Fifi off to her home. That's it, the end. The most fan-loved character loses to the least fan-loved character, in a classic The Bad Guy Wins cartoon ending. It only gets worse if you're aware that the writers actually didn't like Fifi very much, so they enjoyed putting her through the wringer.
The scene from "The Kite" when the kite becomes badly damaged in a storm, causing its moth companion to cry. The depressing violin music that plays in the background doesn't help either.
The ending of "Washingtoon", where the evil Moral Guardian is reunited with her "tooniness", who she hasn't seen in years. This gives her a sense of humor and she bounces off happily to Wackyland.
Just before Buster and Babs go to appeal before Congress, they stop in at the Lincoln Memorial. Babs reads off a quote from the Gettysburg Address, when Buster admits that it doesn't apply to toons and that they were a "lost cause." What follows can be considered the greatest motivational moment of Western Animation.
Abraham Lincoln: "Lost causes are the only causes worth fighting for... Stand tough in the face of adversity, let right be done, let truth be your guide, and most of all, never give up. Never EVER give up."
It turns out to be Reagan talking to his doll, but his rambling still motivated them.
"Night of the Living Pets" has a Downer Beginning with Elmyra looking through a photo album of all the (good?) times she had with her now-deceased pets. Even though she was obviously the cause of their deaths, the poor thing looks like she was about to burst into tears any minute.
Meta example: The death of Plucky's voice actor, Joe Alaskey, on February 4th, 2016 from Cancer.
When you think about it, the tale of One Eyed Jack in "The Horror Of Slumber Party Mountain". Basically, One Eyed Jack was born deformed and treated like garbage, hit by a car and taxedermied into an even uglier "freak". Even if "One Eyed Jack" turned out to be Elmyra in a costume in the end, just imagine if there's still a real One Eyed Jack out there and if there is, he's without a doubt the biggest Woobie in the series. Even moreso than Furball because at least Furball is friends with the main gang whereas poor Jack grew up without a single friend. Ouch.
In "It's a Wonderful Cartoon Show", a depressed Buster was contemplating suicide by tossing himself off the film reel. All because he felt he made a mess of things. Then when the mysterious White Rabbit showed him a Tiny Toons where he never existed...
It was bad enough that Acme Acres had gotten taken over by Montana Max, but the show itself was taken over by Plucky, who basically made it nothing more than shameless self-promoting. He made all the rest of the cast his personal butt monkeys, going especially hard on Babs. Plucky had always been a Jerkass, but he Took a Level in Jerkass with the way he sadistically victimizes Babs every few seconds for no reason other than his own amusement, completely unprovoked. The sad thing is that Babs had none of her spunky bravado and was completely submissive about the abuse she goes through. It's like she's completely given up on life.
In the theater, Buster finds Babs watching some old cartoon clips while wishing she could co-host with someone who actually cares about her. Buster then encounters her and tries to remind her of who he is, of who they are, that they're the stars of Tiny Toons. But instead...
Babs: You're crazy! Plucky's the star! Who are you!? You're stalking me, aren't you!? GO AWAY! LEAVE ME ALONE!
Just Buster feeling crushed about the above, the one person he cared about more than anyone running from him in fear. All he wanted was for Babs to at least be spared from all the misery, but that hope was dashed. He was downright horrified how Babs' life turned out without him.
From "Rock 'N' Roar":
While looking for his soccer ball, Buster finds an egg that hatches into a dinosaur, which he names "Rover" and decides to keep as a pet. After unsuccessfully trying to feed him vegetables, Buster finds out that Rover is a T-Rex which mostly eats smaller mammals. Since he has no meat byproducts, he willingly lets Rover eat him and says, "Good night, son.". Fortunately, Rover has a change of heart and agrees to let Buster feed him vegetables.
Near the end of the episode, Buster returns to the cave where he found Rover's egg. When Rover roars, he opens a door leading to a prehistoric paradise where his brothers and sisters live. Wanting to protect Rover from Montana Max, Buster tells Rover that's where he belongs. Rover wants to stay with Buster, but Buster tells him that if he does, Monty will hunt him for the rest of his life. Afterwards, the two say good-bye to each other.