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Tear Jerker: X-Men: Evolution
In "Shadowed Past", Professor X visits Mystique to discuss recent events involving her son Kurt and asks her, "Was It Really Worth It?" The episode ends with Mystique watching a mother hug her daughter goodbye as she drops her off at school.
In a flashback (which Rogue first misinterprets as a dream) it's shown that unlike most of her other incarnations, she accidentally lost Kurt after trying to find a way to treat his mutation.
And speaking of that happy little family, the episode where Mystique has been turned to stone and Rogue, in a fit of rage, pushes the statue off a cliff onto rocks below. Kurt screams "NOOOO!" and bamfs down to get her, but it's too late... Nightcrawler's Big "NO!" might have sounded Narmy to some, but to others...
In the episode that introduced X-23, her Back Story was virtually nothing but this. Then we have her breaking down during her conversation with Wolverine...
To solidify this, just look at the HYDRA employee who tells Wolverine about her and her involvement in X-23's creation and life. Wolverine is outraged and demands to know how this woman sleeps at night. Her response: "I don't."
The Christmas episode:
An apartment building is burning down on Christmas and a teenage girl is desperately trying to get inside and save her mother, crying and screaming since the lady in a wheelchair and cannot escape on her own.
Girl: My mom is still inside! She can't walk! She's in a wheelchair! Please let me go inside and save her, MOMMY!
In a Crowning Moment of Heartwarming (and a huge moment of relief), Angel saves the lady and places her gently on a nearby bench, and soon she's reunited with her daughter.
The last couple minutes of the Christmas Episode of X-Men: Evolution definitely qualifies. It goes from a little girl who was saved by the vigilante Angel finally coming out of a coma and saying to her parents "My angel - he came to see me", complete with Rogue shedding a few tears, to a montage of various characters celebrating the holidays in their own way. Nightcrawler is seen embracing his parents (whom he hasn't seen for the entire first season and a good part of the second) in the airport, and near the end Wolverine is completely alone in a bar, playing pool. And there is piano music playing over all of this.
"Been a long time, Cap, but I'm still fightin' the good fight. Today we had a victory... for you. You gotta know we'll find that cure; I promise you that. Because you and me... you and me, we made a great team. Yeah... I'll be here when you get out."
Professor X's speech at the end of the Grand Finale, especially the part with Jean turning into the Phoenix.
"The Cauldron". Scott's flash back to his parent's death and being seperated from his brother, to a later scene where Jean tells him she doesn't want to know him anymore since he used Magneto's power machine and is now, against his will, bound to being loyal to him, to the point of attacking his friends.
Adding to that, has anyone ever seen that X-Men art meme? Near the bottom two questions are directed at Cyclops, one is 'why do you think he's so uptight' and 'why don't we prank him'. Normally this is served for some lighthearted (Or ocasionally mean spirited) jokes directed at him. However one time one person answered them respectfully with 'My parents died' and 'Dude! His parents DIED!' It's quite sad yet reassuring that some people do pity him.