The Song of Healing, particularly coupled with Darmani's cutscene, is extremely sad. I also think the Final Hour from MM is extremely depressing. Finally, Queen Rutela's theme.
Most of Majora’s Mask is sad. The other songs that came to mind are both from said game: Song of Healing and Astral Observatory. I feel so sad when I especially hear the latter. It has something dreamy, but also something sad, longing, lonely. It’s a very complex piece. I’m not sure who composed it, though. Koji Kondo or Toru Minegishi? Is there some wiki explaining what part of the soundtrack each of the two composers did for the OST?
I don't remember what it's called, but the song that plays when Midna is dying in Twilight Princess. That whole part of the game is depressing, and that song just added to that feeling.
To me it shall always be "the final hour". Never have I heard such a tearful song. It really feels like the entire world is going to die, the Innocence destroyed and no-more.