As a warning before I start, I'll have you know that I always pick ones intended to make people cringe. (Sadly, too many people have 'popularized' Aeris x Sephiroth for me to ever use that one.)
Let's start off easy and reiterate one mentioned earlier, Hope x Lightning. Y'know, Hope's at that age where he's at the mercy of his hormones. In many ways, Hope sort of sees Lightning as a surrogate mother, and Lightning probably thinks of Hope as the son she never had. Combine all this tension with their isolation from the rest of Cocoon society and the foreboding dread that they don't have long to live thanks to their Focus... much like Shinji and Misato in Evangelion, the tension no doubt led to one of them making a move in an attempt to comfort the other, and there's no reason to believe that the other rejected it. No doubt, the theory will be confirmed and elaborated upon in the eventual compilation game, Final Fantasy 30.
Bartz x Lenna x Faris x Krile. Bartz is the pimp; women want to be with him, and men want to be him. Ok, not so cringe inducing, but no doubt there's someone who would be offended by it.
Squall x Ultimacea. All she really wants is a little love, and... well, Squall isn't the best place to go for affection. But! At least Ultimacea won't be as creepy a girlfriend as Rinoa sometimes is.
Cecil x Kain. Sure, he leads you to believe that he's jealous of Cecil for getting Rosa, but in all reality, Kain is really jealous of Rosa for getting Cecil. All those times he kidnapped her for Golbez? He was really trying to take out his competition.
Palom and Porom! Their names are alliterative, its perfect! They already bicker like an old married couple.
Kefka x Harley Quinn. Sure, this one breaks the rules by going outside the Final Fantasy series, but let's face it, Kefka has ambition where the Joker lacks it. Terrorize a city? Why not the entire world? And if that's the kind of thing that gets Harley off, then Kefka ought to be her go-to guy.
And not mine, but still the greatest... Matoya x Bahamut. Don't ask what the rat tail was for.
This is harder than I thought, I'll have to try and come up with more.