This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Dr. Horrible's Sing-Along Blog
Penny's death. Even though we all knew it was coming, because as we all know, Joss Whedon Hates Happiness, that doesn't make it any less awful. To make it all the worse, she did not see it coming. Maybe Joss Whedon's name in the credits was a bit of a hint but, honestly, you don't expect something with a title like that and a screamingly funny first and second act to have such a collosal Downer Ending. Even more, Penny's final words "Captain Hammer will save us" and just the look on Dr. Horrible's face.
[singing] "And I won't feel ... a thing."
What make that last moment a true Tearjerker is Neil Patrick Harris' acting. In that one moment, he moves from singing triumphantly, to a dull near-muttering of the final two words, alone. In his lab, no costume, no act, simply staring at the camera. It really shows that despite his 'victory', he truly feels that he's lost everything. Just... wow. And a bit before that, during his triumphant "evil" last stanza, you can hear the soft "everything you ever" still making its way through...
The credits. No, really. About 5-10 seconds of dead silence during which to process that heart-wrencher ending, followed by a hauntingly gorgeous rendition of the theme music on violin. Even worse, it begins with Penny's theme and is then drowned out by Dr. Horrible's.
How about that newspaper headline: "Community mourns what's-her-name." The only reason anyone notices Penny's death is because she was Captain Hammer's girlfriend. Nobody cares about her work for the homeless, or her sweet personality - maybe nobody even knows what she does. The only one who knows is Billy/Dr. Horrible, and... and...
Billy staring into the camera for several seconds at the start of Act 2. He's been having trouble just attempting to TALK to Penny, and all Hammer had to do was look at her (after he threw her in the garbage and just looked to stop the van that was barrelling toward her) in order to get her to invite him out. This is one that just about anyone who Cannot Spit It Out will relate to, it's just the later Tear Jerkers drown it out.
The finale is just one huge Tear Jerker, but one of the most powerful moments is when the slow, mournful "Everything You Ever" melody gives way to a brief reprise of "Brand New Day," as we see Dr. Horrible making his way to the ELE. That one musical cue just emphasizes how far Billy's fallen and makes it even sadder to see.
Pay attention to Penny during the end of Slipping, after Dr Horrible sings "head up Billy buddy," and Penny stands up she murmurs the words "Billy buddy". Her expression of disbelief while she said it is heartbreaking. (She might also be saying "Billy? Oh, no..." Either way, however, the effect is the same).
Penny sitting in the laundromat waiting for Billy, with two frozen yogurts in front of her. Meanwhile, Dr. Horrible is busy working on his death ray to murder Captain Hammer and win Penny's love.
Which sums up the ironic tragedy of the entire story. If Billy had just been himself and been patient Penny would have eventually realized Captain Hammer was a jerk and left him on her own, and possibly would have come to like Billy as more than just a friend. But because he has no faith in himself (or her) he throws himself into his secret identity, believing it's the only way he can win... and ends up destroying everything he wants in his attempt to achieve it.
In fact even before that, we see proof that she could have eventually chosen him. In "Brand New Day", Billy sings, "And Penny will see the evil me, not a joke, not a dork, not a failure"- but Penny herself never saw him as such or made him feel like she did. She has always been kind to him, which could be just her generic kindness fitting someone volunteering with the homeless, but it does definitely give weight both to the theory that she could have warmed up to him romantically if he stayed himself, and to theories saying that Billy projected a lot into her, but in another fashion, he projected his own insecurities born of years of beating and failure onto her.
The line The world I wanted at my feet... in the song 'Everything you Ever' as Dr Horrible stands over Penny's dead body.
Which serves as a Call-Back to the opening song, "Laundry Day", when he sings "With my Freeze Ray I will/Stop... the world." and the only thing that stops moving is Penny (and her laundry), hinting that Penny, and the one thing that brought them together, were his world.
When Billy rushes over to Penny, and despite the fact that Penny is very near-death, she asks if he's okay.
It's rather simple and if you lose attention for even a moment, you'd miss it. During "Slipping", Dr. Horrible breaks from his villain song to tell a person nearby how to spell his name. "Yeah, it's two Rs, H-O-R-R, right-" If one really thinks about it, this is sad in more than one way. Not only does he feel the need to make sure people know how to spell his name. As a young nerd who had every reason to view himself as intellectually superior to his peers, he grew into a man who didn't chastise this person who was writing down his name, he didn't even lift up his head and gloat like he was proud of his name and wanted them to remember it properly. He politely helped them out. While he was having his big moment, he took the time to help out a person who must seem rather dull by comparison, not knowing how to spell that simple word. In this two minute scene where he goes on an ego-trip wherein he aggrandizes himself and says that the world is going to burn, he's still a kind and soft-spoken individual willing to help. It really wasn't about being evil, taking over the world as a true villain. He just wanted revenge against Cpt. Hammer. His anger was directed solely at his one true abuser. And when he had his chance to finish him off? He stared at him, unable to pull the trigger. If not for Penny's death, he'd still have had a chance at happiness.
When Penny has a second frozen yoghurt and keeps looking at the door but Billy doesn't turn up. If Horrible hadn't been trying to get revenge, she might have chosen him.
Penny's Song. "Here's the story of a girl, who grew up lost and lonely..."
This part of "So They Say:"
Dr. Horrible and Penny: There's no happy ending, so they say.
Dr. Horrible: Not for me, anyway...
"Caring Hands" is only thirty seconds long, but it still manages to tug at the heartstrings, and is a perfect Establishing Character Moment for Penny. She stands on a street corner, trying to get people to sign her petition so she can open a homeless shelter, and absolutely no one pays any attention to her, let alone stops to sign their name. She doesn't let it get her down, but it does prove how the people in this universe don't care about the real, genuinely good and honest people like Penny.
Would you lend a caring hand to shelter those who need it? Only have to sign your name. Don't even have to read it... Would you help? Nope? ... How 'bout you?