I didn't know this thread existed until now, and since I'm currently playing Star--er, FFXII, I have to put in my 20 cents.
Lithium, I agree with you on that you can ship the characters together in several different ways and, oddly enough, you could see most of them working out.
My thoughts on Balthier/Fran: I think the fact that they have this unbreakable bond is the best part, whether or not they're just buddies/comrades or whether they've been in a relationship or actually ARE in one during the game.
However, saying that, I always felt they were more than just comrades. I think a couple parts between the two makes it seem like they are in a sort of romantic relationship. Not one where they're making out in public, but it seems so... I dunno, subtle. Like they don't have to show it off for it to be there, they don't have to tell people or anything. It's just there, between the two of them.
Now, interesting to note, there's an NPC in Rabanastre's aerodome that comments on seeing Baltheir standing nearby. He says Balthier is the most famous sky pirate and whatnot for the deeds he's done, but stops short of mentioning them all, instead ending with "But you'll have to wait until you're older to hear those." Makes me think Baltheir's probably stolen some women's virginity or something close.
Now this does seem like him, so does this mean him and Fran are not in any romantic relationship? Well it is open to interpretation in the game, but to me, it just seems like they're together in that way to me.
Like someone above said, not like a 'married' relationship, but still, they seem like soul mates to me in a way.
Oh, and Ashe... at times she seems like she could go with Vaan or Baltheir, but I never pictured her with Basch.
I'll keep playing and see if there's anything worth noting in the game between them.
She just seems hung up on Rossler. Which is kind of nice, as it shows she actually loved him, but it doesn't open up much room for other romances.
Vaan and penelo is canon, right? But Penelo and Larsa are cute together...
When I first played the game, I thought those two would get into a relationship in the future. As for Vaan and Penelo, they do seem like friends forever or childhood-friends-turned-sweethearts.
As for that being odd to some, at least it's the childhood sweetheart taking over sibling-like relationship, and not them becoming sweethearts but finding out their siblings.