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Tear Jerker: X-Men: First Class
The first time Charles and Erik meet. Erik's expression and the way he says "I thought I was alone!" was just heart-wrenching. He finally meets someone like him in the world and it's just so emotionally overwhelming for him. Bonus points for the Sub Text - Erik has already said earlier in the movie, in reference to the Nazi Gold he was holding, that his people were wiped out for this, implying that he was the only survivor.
Pretty much every time Erik and Charles have a meaningful conversation. The scene where Charles gives Erik inner peace by reaching into Erik's mind and helping him remember his brightest memory, one of his dead mother, causing both of them to cry comes to mind.
When Charles is paralyzed thanks to Erik. It's an accident, but both of their reactions are heartbreaking, especially Erik's. "I want you on my side."
The fact that Erik leaves before he even learns that Charles is paralyzed. If he'd heard Charles say "I can't feel my legs", don't you think he might've stayed? The way he said it was absolutely heartbreaking....
The first meeting of young Charles and the young Mystique. "You never have to steal. Ever again."
Which of course makes the scene when Mystique leaves Charles to go with Erik all the more heartbreaking. She kisses him on the forehead and leaves. Dear GOD, what might have been....
Alex watching Darwin pretty much burn from the inside out. It's the way they look at each other until they can't.
Keep in mind, as the base is attacked, Darwin was always standing in front of the group, trying to shield them from anyone who might have tried to hurt them. That's what he was still doing when he was killed. He was a teenager living an ordinary life, and then he died to save some friends who were like him.
Hank and Charles being jerks to Raven; Charles is a naive hypocrite, and Hank is skeptical about mutants being accepted.
The Foregone Conclusion of Mystique's storyline. She is loyal to Erik for many, many years, doing whatever he asks. Including, in the first film, poisoning Charles. And then, in X3, he abandons her the moment she loses her mutation.