As much as I love JRPGs, they have pretty silly stories. I'm usually in it more for the characters than anything else. Final Fantasy VIII is dear to my heart, but I have a love/hate relationship with the story. Disc 1 contains some of the best few hours of gaming I've ever experienced. I loved the rivalry between Squall and Seifer. I found Seifer's motivations to be fresh for a JRPG, and very human. When I firs played the game, I easily related with Squall, as both of us had a tough time talking to pretty brunettes. Then disc two waltzes on in, throws in the whole GF making every character forget that they've known each other since childhood and now they've been reunited to save the world and time traveling witches and NORG. It's just awful.
FFIX was good. The game focuses on each character and their individual struggles. I loved the way the game explores existence, with Zidane and Vivi having both been created.
Oh, and I'll throw out a curve ball: Paper Mario 2. Less for the main plot, which is the same as most other Mario games. I loved how each chapter of the game was a fun, self-contained story, each with its own quirks and names for Mario. There was also the subplot where the AI falls in love with Peach. TTYD is a seriously underrated game.