Rinoa, pretty much for the reasons Valentines stated. She's just this upper-class girl who wanted to save her town and ended up getting in over her head. She tried, though. She's straightforward and bold and says what she feels, and even though she openly admits to being scared of the crazy things she's been thrown into, she braves it out and continues onward. Rinoa's stronger than people give her credit for, I think. She's also teenagey and immature sometimes, but I find it endearing.
I also love Rikku. She's cute, energetic and spunky and has no qualms about being a bit of a smartass sometimes. What I found interesting about her in FFX was that her cheerful attitude masked an underlying sadness-- her people were widely hated, she lost her home, and she thought she was going to lose her cousin/best friend. She hid it until she couldn't; most notable, for me, was the scene on Gagazet where she tells Yuna to stop her pilgrimage ("don't talk like that, Yunie. We'll see each other again someday, okay?"). She's also pretty smart, what with her handling of technology and all that.
"Now I am become Death, Destroyer Of Worlds" - J. Robert Oppenheimer/Bhagavad Gita
It's between Edge and Locke. Both characters have such great personalities within their game, and they both end up being heroes despite what they started out to do, one to avenge his parents and the other to revive his fallen love. Both fail at their mission, and yet struggle on, accepting this and become greater for it.
I really connected with almost all the characters from FF4 - FF10 so it's hard to pick my absolute favourite one. I'd have to say though that one of my very favourite characters was Kain from FF4. Throughout the game he'd be good, then evil, then good again and then back to being evil. Thing is though, he was such a good fighter and kicked so much ass when in your party, you were so grateful when he was back in your team again. Then right at the end of the game when you're gonna head off to fight zeromus, he rejoins your party and becomes a good guy for good. Quality character who was as hard as nails and came good right when you needed him!!