Okay, just as a warning, you have someone here who deals with fanfic a lot. First, though to deal with the original poster's question: In the game, there's just the couples mentioned.

Obviously, there's Squall and Rinoa; y'know, major plot point in the game and all. Irvine and Selphie are implied to have a connection, but whether it's going to last or not is up in the air, given their personalities and the way that they started in the first place. It's semi-popular to pair Irvine and Quistis, and I can probably talk more on that if you want to know.

I saw him mentioned, but I don't actually think that Seifer ends up with anyone or has a start during the game (though before the game, Rinoa and Seifer dated, and it might have been interesting if Square had focused more on what that means for Squall and Rinoa, with Seifer and Squall being rivals and all)--there are those that think that there was more of a relationship (on a very ugly level) between Seifer and Ultimecia, but that's a matter of taste more than anything else. Fuujin and Raijin, on the other hand, are probably closer to siblings. Really.

Edea and Cid deserve another mention, because Cid in particular is really very underrated as a character.

I really don't think that Quistis and Zell have a chance of being romantically involved, though. The problem is that Quistis sees Zell as a student, throughout the game--there's a power difference there, even if it's just in their minds. To each other, they're 'Instructor' and 'student', as much as they are 'Quistis' and 'Zell'. That's simply not a foundation for a relationship. As for Quistis and Squall, Squall is with Rinoa, and it's my opinion that Quistis didn't want Squall but the idea of Squall--it seems to me that she wasn't lying at Trabia Garden, but that she's really not that well-acquainted with her own feelings on such matters. But that's another topic.

Personally, I think Quistis and Xu would be a good match, but it would have to happen after the ending, as they're close friends at most during the game. It makes a good deal more sense than a lot of couples people come up with in stories.