I recently watched The Tale Of Princess Kaguya. The music of the Celestial Beings (Part I,Part II) definitely brings tears now. It's so pretty and joyful, but in the movie it essentially represents the "death" of a beloved character.
I can't find the track anywhere on youtube, but there's also a sad/strings version of the Silver Spoon anime's main theme that makes me cry like a baby, because it's played over the scene where
one of the characters loses their family farm and is forced to sell all their animals
And in not-anime, Zelda's Lullaby from the LoZ games also makes me cry now. It's always been my favorite piece and the Skyward Sword version of it is so pretty and sad ;___;