Well that would be in my favorite Final fantasy game of all time, FFX. That was the first and last Final Fantasy I played and actually grew a relationship with the characters.

The biggest moments to me was when I found out Tidus was part of a dream world and goes through an epic battle with Sin.
Just for him to start disappearing just before Yuna hugs him.

I have a lot of major moments in that game, as I feel Square Soft did a great job building the characters throughout the story. That's the only reason I tried out FFX-2 once it released. However, that game was nowhere near the great FFX and it was very boring so I received the bad ending(since I just rushed through it).