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The death of Jonathan's dog, Danny, is particularly crushing because the animal was the closest thing Jonathan had to a friend, and it's even sadder because of how easily it could have been prevented. The dog died only because Dio lost against Jonathan in a fair fight, and he got him killed in the cruelest way possible. note To clarify: stuffing him inside the outside furnace and him being muffled; thus one of the servants wouldn't know that they were unknowingly burning Danny alive. The first truly saddening moment in the series underscores just how much of a bastard Dio is.
The football game that Jonathan and Dio had won. They both act like they've gotten over their rivalry and truly became brothers. Dio of course internally mocks Jonathan. Jonathan can't even imagine that Dio could be anything but the monster he was and still is from their childhood... and he feels horribly guilty for being suspicious despite the fact that he's right to.
At the beginning of the Genre Shift, George Joestar protects Jonathan from Dio's dagger, and then dies in his arms. This is after making a speech on how he was sorry he was so hard on him since his youth.
Bruford's tragic backstory, as well as his inevitable fate: Both he and Tarkus sacrificed themselves in order to save their master, Queen Mary, but Reality Ensues since Elizabeth, her political rival had already had her killed. With the revelation of their Senseless Sacrifice, it's little wonder why both he and especially Tarkus lost faith in humanity and became easy for Dio to control.
The death of Will Zeppeli. He knew he was inevitably going to die the way he did, so he used it to Jonathan's advantage.
The death of Jonathan Joestar: he dies to save Erina, his beloved wife and childhood sweetheart, an infant of a woman killed by a zombie to which he had no connections to, and his unborn child, on his honeymoon no less, taking Dio down to the bottom of the sea with him. Made all the sadder by the smile on his face when he dies, directed at his wife, the readers, and Dio himself.
There's also the fact that in the end, even after all the damage Dio did, Jonathan was able to forgive him and call their relationship a "bizarre friendship". He even felt sorrow for when he thought he was dead after beating him finally. Talk about Too Good for This Sinful Earth.
And then his last words to Erina are even more heart-wrenching:
Somehow, even Dio makes the scene more sorrowful. He rants about his situation, about the ludicrousness of Jonathan's suicidal strategy, all while his head is cradled in his arms... and then he realizes that Jonathan has just died. The look of shock and then sadness on his face proves that as much as Dio loved boasting how his vampirism put him above normal humans, in these last moments he was as human as any man.