I had the same experience.
I would say Nanaki learing about his father, but in the interest of variety, I'll say when Tifa wakes up after Northern Crater. Our heroes are captured, Cloud is missing, they're about to be executed for no real reason, a giant meteor is coming to destroy the majority of life on the planet, and the world is being torn apart by giant kaiju. When I first played it, my reaction was, "....Jesus!!"