I think the opening to Ys 4 is my favorite overall. I loved watching the events that transpired at the close of Ys 2. It gave me tons of nostalgic feelings when I first saw it many years ago and I feel that it aged very well and continues to look great today.
I never played all the way through the game, but the intro to 3x3 Eyes always looked great in my opinion. Tons of fluid animation and it was the clearest example I can think of to demonstrate the potential differences between what an arcade cd game and a super cd game could do.
I guess in third place I'd put the intro to Ys 1. I showed it to all of my friends and used it to explain why CDs were the future of video games. There was something magical about seeing that intro when I saw it; there was nothing else comparable.