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Tear Jerker: King Kong
The death of Kong. Yes, It Was His Sled applies in full, but the two main versions still wring it out for all its worth. The 1933 version had this happen unintentionally, as technically, Kong is the villain, but the way the music is used and the "Performance" Willis O'Brian gives Kong really rank up the sympathy, and though it's inevitable—everyone still felt sorry for the poor beast. The 2005 version's music and performance are equally evocative.
You can argue that Kong being so sympathetic wasn't unintentional. You can argue the original is designed to be a tragedy; even when the monster is killed, the famous last line makes it that there's no sense of accomplishment or victory. In the end, you can only feel heartbroken for Kong.
Baby Kong using the last moments of his life to save Carl Denham from drowning, as he himself is drowned.
The coffee-table book A Natural History Of Skull Island, in its description of Kong's species, includes a heartbreaking illustration of an orphaned baby Kong, uncomprehendingly clutching the fur of his dead mother. See it here, in the lower righthand corner.
Jimmy's reaction to Hayes' death.
Also, Lumpy's reaction to Choy's.
"It was Beauty killed the Beast."
How is it that in this whole movie the person you sympathize most with is Jack Black's ruthless film director? Virtually everything he did from the moment someone tells us that his character "destroys everything he loves" was given such a heartbreaking gravitas as we realize that he really does care about things (including the monkey) and yet he never changes his course of action to save it.
The scene of Ann and Kong in Central Park, because it showed that they were far more than their archetypes of damsel in distress and monster. The tear jerker factor here derives from the fact that we know how the film will end (like the remake would change it), and so know that there is no hope for a happy ending for them.
1933 and 2005 versions of Kong's final battle on the Empire State Building. His last moments are spent looking at Ann for comfort and then the last plane swoops in and...(sob)
Seventeen people died to rescue Ann, yet she only cares about Kong. All the Too Cool to Live characters like Lumpy and Hayes died and she doesn't even care.
For that matter, neither did Jack. Seventeen people died to save his girlfriend, the thing was his idea, and he never once appeared to give a second thought about them, going so far as to scornfully deride actor Bruce Baxter for seeing what a Fool's Errand the whole thing was.
To be fair, some of them died before they even reached Anne. She probably didn't understand how costly the rescue mission had been until later. Plus, her protests when they capture Kong may not have been entirely for Kong's sake: she'd seen Kong beat down multiple V. rexes when he was angry, so could've feared that taking him prisoner might cost still more men their lives.
The original 1933 version gives her a more plausible reason for not spending to much screen time on grieving. She usually spent her time scared to death!
The scene where Kong and Anne are sliding on the frozen lake, happy and laughing and then the army starts shooting at them again.
Sure the 70s remake isn't that good and it may come too little too late but Kong getting gunned down by helicopters, a total blood bath, and then falling to his seemingly death is pretty sad. Also the pilots of the planes/helicopter that perished since like it or not it is pretty dangerous having an animal that big on the loose.