This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The League of Extraordinary Gentlemen
The death of Hyde was definitely not your standard tear jerker. Hyde was a monster, and he knew it, completely denying and shooting down anything that would make him sympathetic (his feelings for Mina being love, any desire he might have had to save the world), but somehow him destroying the Martians after saying goodbye to Mina and going to his inevitable death singing and dancing ended up looking really noble. He was an awful person, but he did heroic things; a true anti-hero. Then they named a park after him. You know the one.
Hyde and Mina's final goodbye. All he asks of her is for her to let him kiss her and to let him touch her breasts. Throughout the second volume, Mina was the one and only person that the monster Hyde remotely liked, maybe loved. He even states so himself thatout of all mankind, Mina is the only person he cares about, because she's the only one who sees him as a man, albeit an evil man. Because she has met somebody far worse.
Hyde (leaving to fight the Martians): Goodbye, my perfect Mina.
The death of poor Dr Jekyll. Like in the original story, he doesnt even get to die as himself, he is simply submerged into Hyde and disappears forever.
Griffin's betrayal has a notably horrific moment when he strikes Mina down, steals the plans from her, and forces her to degrade herself before he departs. Seeing her in such a broken state is pretty damn depressing, especially so when Hyde finds her and legitimately freaks out over her collapsed form.
The Downer Ending of the book with two fifths of the team dead, Nemo going off the team after The British Government developing bio-weapons to fight the Martians with Alan and Mina unaware they were carrying said weapons and Mina leaving Allan to clear her head in Scotland after the entire situation is done with. The final panel is Allan, sitting defeated on a park bench with leaves falling around him.
Orlando's account of his/her past has moments of this, most notably his/her sadness over never seeing Sinbad, whom he/she considered his/her true love amongst countless others, ever again following the sailor's Eight Voyage.
He's a hotblooded racist, for sure, but Hugo Drummond deeply cared for his goddaughter, Emma Night. So when he's informed that "Jimmy" Bond murdered her father, who was also a good friend of his, Drummond flies into a rage and attacks him. Sadly, Bond shoots Drummond in the knee and then in the head while he's down. To make it even worse, Bond gloats to Drummond before he kills him about how he'll be a hero and screw Emma, all while she's unaware of Bond's actions.
The Century Trilogy
Janni started out as a woman who defied her father's request to continue his tradition as a terrorist. But then she is raped in 1910, which sadly prompts her Heel–Face Turn, and results in her becoming a bigger monster than her father had been. And as seen in the examples of the Nemo spinoffs below, her life gets much sadder.
The massacre at Hogwarts, committed by Harry himself, is bound to cause such a response from fans of the franchise. And even then, there are pretty horrific sequences, like Ron and Hermoine begging for their lives moments before they're killed.
As much of an ass he is, and as horrible as the acts he commits are, there is still a sadness to Harry Potter in 2009. The young man had been manipulated towards a horrific destiny as an Antichrist by Oliver Haddo, tried to delay it as long as he could by secluding himself in the long-abandoned Privet Drive, and took as many medications as he can to keep himself in control. He becomes quite pitiable in that regard. On top of that trauma, after all that, Haddo is disappointed with his creation, calling him a "banal antichrist". All of it was for nothing.
By the time of 2009, Allan Quatermain is arguably more of a wreck than he was before. The effects of his immortality have taken hold, and he's vehemently opposed to being the hero ever again due to the massive stress it causes. However, he returns to aid Mina and Orlando by the climax, and even manages to fire off a shot at the Antichrist with his elephant gun. But then, he is killed by the Antichrist in an extremely degrading manner via electrocution as the monster literally urinates lightning. Seeing a hero suffer such a fate is pretty heart-wrenching. If nothing else, his sacrifice was enough to save Mina and Orlando.
Jack rushes in to attack Ayesha, after braving through Hynkel's Metropolis with Janni to save their daughter and son-in-law. He even manages to seize Ayesha by the throat...only to have his head split open by Maria's hand.
The looks of horror on Janni and Jack's faces when they are informed that Hira's craft was shot down say it all. Hira turns out to have survived, but she returns to her mother just in time to be informed of her father's death.