Final Fantasy IX's cutscene where Vivi sends a fireball to the attacking Mage remains etched in my memory. It's an very moving scene which really 'hit the spot' (so to speak) when I first played the game all those years ago.

Final Fantasy X's opening movie is also one of my favourites. The very first glimpse of Blitzball blew me away, and the subsequent arrival of Sin in Zanarkand really impressed me. The music for this cutscene is simply perfect.

Little Big Adventure 2's opening/closing cutscenes are very nice, although they are quite dated now. Great music and cute graphics.

That's all I can think of at the moment. =/