The Magic Tree of Nowhere, where the titular tree is killed by a jealous Eustace.
Remembrance of Courage Past, which shows how Courage met Muriel. Especially with the revelation that his parents were put on a rocket and shot into space by a sadistic vet, with Courage outside the rocket trying to stop it. He escapes the vet by going down a trash chute and you see him land in a dumpster, and he waves to the rocket flying away. Courage has every right to be screwed up and terrified after that.
This whole entire episode can easily chalk up as one of the saddest cartoon episodes most people will ever see, especially with the piano playing
The Curse of Shirley, where a hallucinating Eustace takes pity on a young version of himself.
Eustace, by all means the biggest selfish jerk ever portrayed on any Cartoon Network show.
It's even more sad if you consider that Eustace was seeing this through a mirror that was meant to show one's true self. Sure, it was broken beforehand, but it may have been showing that Eustace is, deep down inside, a sad man who lashes out at everyone due to a painful childhood.
But the one that is considered a Tear Jerker by most viewers is Last of the Starmakers, where Courage has to save the babies of a mother space squid from the military.
"There's no such thing as perfect. You're beautiful just the way you are."— From the episode "Perfect".
"The Hunchback of Nowhere". A lonely and deformed hunchback goes from door to door just seeking shetler only to be called ugly or a freak by everyone, including Eustace, and having them slam the door in his face. He and Courage build a friendship that's both heartwarming and tearjerking as Courage shows the poor soul kindness for once in his life. And the climax only adds to this: as Courage and the Hunchback put on a show for Muriel, Eustace tries to ruin it. The Hunchback's response? He puts on a Eustace mask and forces him to see himself for who he is, which is only more heartrending when you realize that it's not just Eustace: it's for all the people who have said he's just a freak.
"The Queen Of the Black Puddle". It's about a puddle of black water that is actually a passage to another Dimension/World, where there resides a ghastly woman. The woman charms Eustace and takes him to her world, and no surprisingly, Courage doesn't give a damn, and he has all the right not to. But he then sees how Muriel is devastated by having her husband taken from her, crying her heart out, and Courage realizes he'd rather put up with Eustace's crap for the rest of his life than to see his benevolent owner suffer. The episode makes it very clear that Courage saves Eustace, even thought he doesn't deserve it, because his love for Muriel spoke louder than his dislike of Eustace. Undying Loyalty, indeed.
Muriel's weeping over her lost husband is itself quite touching - even though on a day-to-day basis neither of the couple show too much interest or caring for each other, they really seem to share a deep bond of commitment.
Almost all of "The Tower of Dr. Zalost," due in no small part to the haunting soundtrack. Although Dr. Zalost is one of the more cold and ruthless villains on the show, it's hard not to feel bad for a man who is so miserable and lonely that all he can do is lash out at the rest of the world. But if that doesn't evoke any sympathy, the crying baby rat usually does the trick.
There's also a quote from Eustace that basically sums up why he hates Courage so much: "She likes you best, feed her."
There's a very sad moment in "Courage Vs. Mecha Courage", where Courage watches as Muriel sits in her rocking chair while Mecha-Courage sits on her lap, causing Courage to cry.
Downer Ending's from the episode "The Great Fusilli". Sure, the episode's grim ending is played for laughs, as per usual, but when you really think about it, it's actually pretty Tear Jerker: In It, Courage fails to stop Muriel and Eustace from being turned into puppets. But as the show has a Negative Continuity, everything will return to normal.
Observe the relationship between Eustace and his mother, both of them cruel, cold people. Eustace is the way he is due to his mother, and, if one episode in particular is anything to go by, his mother was made this way by a loved one too. Two of the biggest assholes in the show are the result of a cycle of abuse.
The Mask because it tackles the very mature subject of abusive relationships. A talking rabbit named Bunny ended up with an abusive, controlling, gangster asshole named Mad Dog and is not allowed to be with her best friend Kitty anymore. This leads Kitty to believe that all dogs are evil. Now take that last sentience and replace "dogs" with "men". The ending is a Crowning Moment of Heartwarming when Mad Dog gets his just deserts and Bunny and Kitty are reunited.