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Tear Jerker: Rah Xephon
Kamina killing a dolem in Rahxephon, only to find out that Asahina was linked to it and he just killed her as well. And her last words are "Ayato... I love you", spelled out in the lights of the buildings, and not only that - before Asahina died, we could see how she wrote them outas she was dying, desperately trying to relay her last message while Ayato was killing her without knowing it. The episode really went out of its way to milk the scene for as much tragedy as it was worth, fortunately without going too far and just making it cheesy.
This was the only anime that has ever made me cry. I was watching it with anime club and literally everyone was either crying or watching it. Even in the manga my eyes were watering up when that chapter came around.
My personal favourite is "It's not fair! You've known him much longer than I have!"
Adding on to that is "Ayato Kamina! Megumi Shitow used to have a bit of a crush on Ayato Kamina! But she doesn't anymore! That's what she's decided!"
There's also the bit in the last episode where Ayato answers the phone in the sea of mud and sees all of his friends giving him support. His facial expression when Asahina appears says it all.