The cat girls and Folken, Van in the barn dealing with Hitomi and Allen, and the epic final battle followed by Van and Hitomi having to part and never see each other again, because without the pendant she can never return to Gaia.
Dilandau's descent into further insanity, especially in his only scene in episode 16 (Though the German dubbed version of it is SO MUCH MORE heartwrenching in that the woman doing his German voice manages to pull off what I feel is the MOST CONVINCING AND REALISTIC SCREAMING I'VE EVER HEARD in animation! EVER!)
Episode 17. The song "Perfect World" and Allen's talk with his father about life...
The Vision of Escaflowne had a few such scenes revolving around Van and Hitomi.
Even worse, Jajuka's death and his flashbacks to the day when he was separated of his former charge Selena... who would soon become Dilandau.
The look on Van's face when he witnesses Allen kissing Hitomi, it's hard not to feel sorry for him, his face is the expression of a kicked puppy.
The look on Hitomi and Van's faces when they witness Folken's death After he became such a nice guy.....to see his lifeless body falling to the ground, and seeing Van finally screaming "BROTHER!" in a sad tone, without any anger or hate....was too much for me.
The cat girls' death. Their past was pretty sad as well. Hitomi tried so hard to be kind to them and then they died.