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Tear Jerker: Shrek
From the first film:
The Twist Ending of Shrek: "...I'm supposed to be beautiful..." "But you are beautiful."
And don't forget the scene after Shrek and Fiona split up, and everything's going as planned, but both are completely miserable. What really pushes it into tearjerker territory is the heartbreaking "Hallelujah" playing in the background.
The misunderstanding where Shrek overhears Fiona saying, "Who could ever love a beast so hideous and ugly?" is painfully hard to watch. Extra points for being depressing both from Fiona's side and Shrek's side of the conversation.
"I live alone! Me! My swamp! Nobody else, understand? Especially useless, annoying, pathetictalking donkeys!" Just...that. During the whole line, he's obviously trying not to cry, and for once in his life he's let himself have a friend, let himself fall in love, and he thinks it can't be and is trying to shove Donkey out of his life. To make it worse, there's Donkey's clearly-hurt expression and
Donkey: But...I thought—
Shrek: Yeah, well you know what? You thought wrong!
From the second film:
Shrek's Despair Event Horizon. He's left skulling shots ofmilk in the Poison Apple, and lamenting why he even saved Fiona in the first place, alongside Donkey and Puss. It's the lowest we've seen Shrek get, and it is depressing.
Shrek: Look guys, it's for the best. Mom and Dad approve and Fiona gets the man she's always dreamed of. Everybody wins.
Donkey: Except for you. I don't get it, Shrek, you love Fiona.
Shrek: Aye, and that's why I have to let her go.
At the climax, where Shrek and his allies all raid the castle. Mostly, it's just full of the crowner moments for nearly every character but it's the giant Gingerbread Man that gets the tearducts flowing during this scene. His "be good" line was especially tearjerker-worthy...
From the third film:
King Harold's death
Artie explaining about his father abandoning him.
When Shrek get captured by Charming and has to lie to keep Artie from being killed. The music that plays afterwards is on par with Hallelujah in terms of sheer emotion
From the fourth film:
At the end, there's an extended amount of time where it appears that Shrek failed. And, technically speaking, he was dead for a while. This movie being Darker and Edgier than the others, it wasn't unbelievable that they'd do it.
There's also the moment somewhere right after he's beginning to understand what his impulsive wish did - he finds his daughter's doll still in his back pocket from where he'd put it very early on in the film, and the look on his face as he realizes that she doesn't exist anymore is absolutely heartbreaking.
The song "Fiona Doesn't Love Me" and the accompanying scene. Shrek thinks all he has to do to break the spell is get Fiona to kiss him, par the rules of True Love's Kiss. He manages this, but because she doesn't know him that well and thus doesn't love him, nothing happens. Donkey asks him what went wrong, and he has the most despairing look on his face as he says, "But Fiona doesn't love me."