Oh, there are so many to choose from, and hardly any of them come from a Final Fantasy associated with Tetsuya Nomura.
Final Fantasy IV had too many to recount off the top of my head.
Despite FFV's focus on gameplay over narrative, it wasn't without its moments. Galuf's death had a significant effect on me. Gilgamesh's sacrifice was probably the most poignant of the sad moments in FFV. Gilgamesh was awesome.
Final Fantasy VI had some really good ones. The most notable of these was, of course, Cid's death and its effect on Celes. I actually shed tears...more than I ever did for that flower girl. General Leo's death was also quite touching. Watching Kefka pick off the Espers one by one was sad in a sort of horrifying way.
Final Fantasy VII had one sad part, Aeris's demise.
The saddest moment in FFVIII was realizing how uninteresting the game gets after the spectacular end of the first disc.
Final Fantasy IX's saddest moment happens quite early on in the game. Watching the black mages getting snuffed by the Black Waltz was quite profound. Vivi had the best moments in the game, followed closely by Freya. Freya's sad moments were not so melodramatic so much as they were truly sad. To be forgotten is worse than death. People remember you after death, but to be forgotten is like never existing in the first place.
Final Fantasy X's saddest moment was realizing what Auron was.
FFX-2's saddest moment was the very beginnig. Turning Yuna into a popstar is comparable to starving orphans on Christmas.