You know to be honest this one was tough for me to answer.
I love the stories in nearly every game I play because often I only play games with good stories. Now that being said, it would have to be Kingdom Hearts. I love the game play of all of them except Chain of Memories. Birth By Sleep is especially addictive.
But the story? Perhaps it isn't a BAD story necessarily, but it is bat shit crazy. Full of back tracking, stupid turns, idiotic plot devices. I mean really Mickey? A crystal that takes you anywhere, to any time, whenever it or rather the writers feel like it? For shame.