Celes' Suicide Attempt is still my favorite.

Learning about Shadow's Past and relationship with Relm only to see it never conclude.

Vivi Learning his true nature.

The Black Waltz #3 killing the Black Mages in front of Vivi

Auron's death

When Squall finally opens up to the comatose Rinoa

Selphie saying goodbye to her dead friends in Trabia Garden

Zack's death (original version)

Setzer telling the party the story of Daryl

Locke using the Phoenix Esper on Racheal

The Death of the King of Tycoon

Gilgamesh's sacrifice for the party (FFV)

Tellah's death, mainly because the game never hides the fact he was doomed from the beginning.

Baltheir's farewell to Dr. Cid

Fran telling her sister to stay in the Woods and how she lost her ability to hear the spirits.

Basch's story in general.

Sahz's suicide attempt

Cyan seeing his dead family depart on the Phantom Train.

Cyan's dream world, specifically the parts where you can see his memories of his times with his family when you explore the castle.