To say nothing of the dialog after the fight, where in a rare subversion of Gameplay and Story Segregation, the party attempts to save Galuf with spells and items, and fail. No better way to tell the player that this character is truly dead.
Not to mention Krile begging her grandfather not to die and leave her alone, because he's her only living family. And then a few minutes later when she unflinchingly takes his place in the party at his behest.
Syldra makes the most haunting and beautiful noise ever heard, in an SNES game! Not to mention that she gets THREE death scenes!
Gilgamesh as he sacrifices himself to save the main characters from Necrophobe.
There is an optional scene where Bartz visits his hometown, and when he plays music box at his own house... it brings back a very touching scene of his family when his mom about to pass away.
Right before the party heads out for the final confrontation, Exdeath sucks every friend, significant NPC, and character hometown into the Void. In a way it's worse than what any other Final Fantasy villain managed to do, because it's just so personal. Exdeath isn't killing a single hero or NPC who was in his way, he did it just to be cruel.
For those that consider the ending a tearjerker, beat Neo Exdeath with at least one character KOed and bump it by an appropriate factor for each additional character.
If either only Bartz or only Faris /Sarisa survive, it's perhaps the saddest. Bartz started alone and at the end lost everyone all over again. In Faris' case, she's implied to have given up pirating in order to rule Tycoon in Lenna's place.
Krile, telling Mid to take good care of his grandfather.