I've never been much of a shipper really. For some reason, I just don't care for the typical presentation of romance. It almost always seems somewhat unrealistic to me, the extreme, unreasoning passion for another person that is presented as love. For me, true love is something like an extreme version of friendship, or kinship, basically something more reliant on the mind and heart than simple hormones and lustful attraction.
That said, I do enjoy pretty much any pairing that is well written, especially if it's a relationship that involves one of my favorite characters, make sense based on canon material, or is completely and utterly non-sensical. Again, it all depends on how well it is written or presented, which actually holds true for all genres.
I'm a real sucker for family and friendship based stories. For ATLA, interactions between the whole Gaang were amazing, but the relationship between Sokka and Toph was especially note worthy. They seemed like such great buddies, despite their age and other differences, and many fics out there have them wrecking havoc in the most awesome of manners. Sokka and Zuko friendship also has some amazing fiction.
With LOK, I'll probably be looking for the same thing. I already love the brotherly interactions of Mako and Bolin, and the sister-like relationship Korra has with Jinora, Ikki, and Meelo. If my suspicions come true, and the boys wind up living in the Air Temple, I suspect the little ones will treat them as siblings as well, which I would desperately love to see. Despite all of the 'ship-tease' going on, I expect the Ferrets will have an awesome friendship, as legendary as that of the Gaang.
If pressed for an opinion on LOK shipping, I suppose I ship Boliness (BolinxHappiness), which I've seen mentioned in the comment threads for Bolin. I wouldn't mind Borra, but I think I'd love Brorra, which i may have just made up. Basically, I look forward to a bromance relationship between Bolin and Korra, because the two are absolutely adorable together, and Korra could totally be a 'bro' if she wanted to.
I look forward to seeing how things play out.