This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Superman: The Animated Series
As early as the first episode, with Krypton's destruction, which is made even sadder and poignant by the beautiful soundtrack. Right at the beginning of the cataclysm and the arrival of another earthquake comes this exchange:
Patroller: Not another one!
Sul-Van: No. The last one.
"I'm not a freak. I'm not! I'M NOT!"
When Corben realizes how he's lost by becoming Metallo:
Corben: It's all fake. A FRAUD! There's the reality! The metal behind the man! It's all I am now! It's who I am... Metallo.
"Ghost in the Machine": Mercy, trapped under a load of debris, calls to Luthor for help...and he abandons her. The look on her face as she answers his call shows she's been truly shaken.
Lois: I always teased him... But I had so much respect! (in tears) And I liked him too! I really did, I wish I'd told him...
The ending to "Apokolips...Now!" has Superman crying within the episode. Not that the ending wasn't such for the viewers as well...
When Dan Turpin is killed. It's just so freakin' senseless, petty, and above all completely out of nowhere.
"Good-bye, old friend. In the end, the world didn't really need a Superman... just a brave one."
The fact that he's based on the late, great Jack Kirby makes it sting even more.
The otherwise nightmare-inducing Toyman's pop-up book, which details how his innocent, kind-hearted father was tricked into being arrested for mob activity, forcing his son to live a ruined and lonely childhood.
"The boy moved from foster home to foster home, like a little toy that nobody wanted. A childhood is a terrible thing to lose, Ms. Lane..."
The alternate-Superman in "Brave New Metropolis" in his interactions with Lois. His expressions throughout the episode can be surmised as "dead inside".
"You never knew how I felt about you. I didn't know... until you were gone."
The first episode featuring Bizarro ends with him sacrificing himself to hold up Luthor's collapsing clone lab long enough for Superman to save Lois Lane. While he didn't stay dead, it was certainly a powerful moment, especially since it meant Bizarro accepting that he wasn't the real Superman.
Superman discovering the unimaginable magnitude of Brainiac's crimes, and collapsing to his knees in a hologram of one of the dozens of worlds he's destroyed, complete with a powerful circling camera effect.
The end of the whole series, with Superman's brainwashed attack on Metropolis having turned much of the planet against him. Thank god the DCAU continued so this didn't become the actual ending for this version of him.
The whole sequence at the start of "Little Girl Lost" when Superman investigates the remains of his home planet, he comes across a distress signal that leads him to the frozen world Argo. There, he finds a hologram of a scientist named Kala, who explains that Argo had been the sister planet to Krypton. When Krypton was destroyed, it threw Argo out of their suns orbit, killing millions, and dooming the last survivors to a slow death of cold and starvation. Her surviving family was put in stasis and with tears in her eyes, she desperately pleads for rescue. The camera then pans to the pods, all of which have failed... except for Kala's daughter, the future-Supergirl.
Superman: I'm too late...
The people of Apokolips are so broken and bent to the will of Darkseid that when Superman gives him a No-Holds-Barred Beatdown, tossing him to the ground in defeat and declares to the slaves of Apokolips that they're free, they pick Darkseid up to help him heal. They're so far beyond the Despair Event Horizon that they can't even conceive of being without Darkseid, no matter how cruel he is.