I'm not so sure on the definition on Turn-based :S I would think that the Dragon Quest main series games on the ds(i.e IV and V) are turn-based, but since you have the speed attribute on characters I guess you couldn't really call it turnbased since it how fast you get to act depends on your speed. If I've got it wrong then most J/RPG's aren't turn-based, because all of them have the speed/agility attribute on characters :S

Anyway, as stated above, the Dragon Quest games are really good in my opinion, but they are traditional RPGs. That means that it might seem too outdated for you. The stories are good, and they are somewhat independent of eachother. I would in any case recommend DQ IV first. The graphics are cool, but if you have caught the anti-2D sprites illness that seems to have become a pandemic, then there's a possibility that you should stay away from them At least give them a try. They have a little bit of puzzle solving in them.

So since I'm not sure which games are turn-based and not I'll just give you a short list:
Contact (uses touchscreen)
Final Fantasy III (traditional)
Chrono Trigger (ATB-ish system)
Dragon Quest Monsters: Joker (I haven't really played it)
Etrian Odyssey 2 (there's no story relating to the first one I would think. !Addictive and timeconsuming!)
Mario and Luigi: Partners in Time Recommended for ALL new beginners
I've heared some rumors about a game called Zubo. It's supposed to be a bit childish, but most JRPGs have characters that look like children anyway Note that Zubo isn't a JRPG

This post has been edited by Zense, Sun, June 14th, 2009 at 21:26