This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Batman: The Brave and the Bold
Want to know how to make the deaths of Bruce's parents even more depressing? They were gunned down on Christmas in this continuity, after Bruce threw a tantrum over getting a family heirloom of his dad's rather than the Zorro figure he wanted; just knowing he was unwittingly ruining his last ever Christmas with his parents would be tear jerker enough, but the second flashback reveals that the Waynes only went to the movies that night because they were trying to cheer Bruce up about the gift.
And in "Chill of the Night!" Batman gets sent back in time to meet his parents before they died. He gives Martha the biggest hug ever...
The death of Platelet.
G.I. Robot sacrificing itself in the teaser of "The Plague of the Prototypes!" is surprisingly sad.
AQUAMAN'S depression in the beginning of "Mystery in Space!". Seeing the usually exuberant hero who always wants to fight for justice and his friends so down in the dumps, questioning the point of everything he does is really jarring.
Red Tornado makes the Tornado Champion to function as a son. The Tornado Champion becomes the Tornado Tyrant after his hatred of humanity reaches its peak, and Red Tornado is forced to kill his robotic son. Even Red Tornado is saddened by this, and he has no apparent emotion.
What really drives this scene home is what Red Tornado says to Champion before killing him.
Red Tornato: "Declaration: You cannot mock love. For it was love that created YOU."
You can't help but feel sorry for Champion before his Face–Heel Turn. After saving 2 children from a fire, they react in fear of him, and the father accuses him of hurting them. He's saddened by this despite Tornado's attempts to cheer him up, and goes ballistic when Major Disaster attacks Tornado. This causes Tornado to decide to shut him down, and Champion actually pleads, in heartbreaking tones, for him to reconsider. Granted, Champion had already removed the shut-down component from his body, but still... *SOB*
What makes all of this worse? Champion's Face–Heel Turn might not even be his fault, his emotional programing may have been damaged by Major Disaster's cheap shot near the beginning of the episode.
In the Red Tornado's Christmas Episode, he is trying to find the True Meaning of Christmas (and he is trying to do so with the Scientific Method). A kid mentions a "warm tingly feeling", which Batman sagely warns him would, in his case, warrant an immediate trip to get repaired. Thus, when the Red Tornado is damaged, saving the day, he suddenly cheerfully declares that he's experiencing a warm tingly feeling.... *boom*. He gets better, mind you, but if you didn't know that he would get better...
In "The Knights of Tomorrow", when Bruce and Selena are killed by Joker Jr.'s attack on the Batman museum.
Damian blaming himself for it (much like how Bruce himself blames himself for his parents' deaths), because he wouldn't accept his legacy.
The scene where Batman finally meets Joe Chill and reveals his true identity. For Chill, it's something closer to Nightmare Fuel, but it's a Tear Jerker for the audience, for a multitude of reasons: 1) Batman is THIS close to breaking his one rule, he's THAT angry at Chill, and 2) you can tell, that when Batman's looking at Chill, he's reliving the worst night of his entire life.
Batman: "I know because I am the son of the man you murdered! I am Bruce Wayne!
Billy's life in "The Power of Shazam!" is pretty sad: bullies at the orphanage, a strict administrator running the place, and looking on sadly at kids who have parents. He's so certain there's a kinship with Black Adam, but he has to accept in the end that he was wrong. It makes it all the more heartwarming when he finally gets what he wanted most.
Shazam: Captain, what troubles you? Captain Marvel: Black Adam. When I saw that symbol on his chest, I thought I had the chance for a family again. Guess by now I should know better than to get my hopes up like that.
Plastic Man in "Cry of the Freedom Fighters". He just wants to be part of a team and mentions that not even the Justice League was willing to take him. Considering the League in this version has Guy Gardner and Captain Atom as members it's not hard to view it as an intentional snub to Plastic Man.