Not really, there's definitely a story line, and some easter eggs if you've played other entries. However you won't be lost storyline wise if you play them out of order. Except for 1 and 2, they really basically 1 game and should be played in order. If you really liked VIII, VII and Memories of Celceta are the ones that play most similarly to it. VII is on PSP and PC now, while Memories of Celceta is on Vita and coming soon to PC. I think VII might be on sale on steam right now for almost half off. Memories of Celceta is a remake of IV.
If you're interested in trying more classic Ys, there is Ys I and II Chronicles on PC, and PSP, and Oath in Felghana (remake of III) on PC and PSP as well.
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