I've played a lot of JRPGs, and lots were part of series. But I don't think I've been grabbed by many whole series yet (only liked Awakening out of Fire Emblem, only really liked Xillia out of Tales of)

What I can come up with is:

Shining _____ sereis (Force, Darkness, Wisdom, Holy Arc, etc)
Knights of the Old Republic
Mass Effect
Dragon Age

Other than a couple of Elder Scrolls or Diablo games, I can't really think of anything. And those were more just fun time wasters. Extremely fun and well built time wasters. But for me to say "I really enjoyed that RPG" I feel like it has to have a more gripping narrative and I probably should have actually beaten it. I haven't beaten any Bethesda games, or any Baldur's Gate or anything