DemyxZexion
I have such an unnatural attraction to this pairing. Out of every pairing I've ever loved I have to say that this is my OTP. I don't exactly remember when I began to like this pairing, but I remember just having a brief idea that they'd b good together, looked it up on Fanfiction.net and Deviant art and low and behold IT EXISTED! (and by existed I mean I wasn't alone in thinking they'd be pretty awesome together). To be honest any Organization XIII member with another member is not an impossible pairing so it's not all that far-fetched in my eyes.
There's something really sweet and forbidden about two people who are pretty opposite of each other finding a way to be together and make things work. In my eyes, I see it this way; Demyx is a slacker and a goof off, while Zexion is hard working and detached emotionally. I believe that Demyx's laid back attitude would eventually rub off on Zexion and soften how strict and tight he is while Zexion would keep Demyx in line. I just really like how they would be able to balance each other out. I always think of the dynamics of their relationship as being the same as mine and my boyfriends. I'm a work-a-holic who's motivated and largely unemotional while he's very energetic (overly energetic most of the damn time), lazy, and silly. We have a lot of fights and quarrels over how our lifestyles clash, but over-all we balance each other out perfectly and by the end of the day, really love each other.
I always use our relationship to justify why I ship this and how it can work.
In short, best pairing ever man.
AxelRoxas
My close second. Seriously, It's obvious in every game and it's just the sweetest pairing ever. Axel really cares for Roxas so much. I even remember reading somewhere (totally don't have the source anymore) that they actually DID write Axel and Roxas as really being in a relationship but Disney didn't allow it because it was too ballsy (Disney just doesn't have the globin that square has :] ). They still kept the relationship there, but made it more subtle and acceptable for an american audience. After playing 358/2 days and reading the novel, there's no way you can deny that this is legit and beautiful.
Other favorite random pairings.
Sora/Namine
Marluxia/Larxene
Ventus/Vanitas