I came up with these very quickly, so I'm willing (in fact, eager) to hear what other people think about these, and about characters who aren't on the list yet.
Stannis Baratheon: Lawful Neutral
Ned Stark: Lawful Good
Balon Greyjoy: Chaotic Neutral
Daenerys Targaryen: Chaotic Good
Jaqen H'ghar: Chaotic Neutral
Tyrion Lannister: Neutral Good
Brienne of Tarth: Lawful Good
Jaime Lannister: Neutral Evil --> True Neutral
Theon Greyjoy: Confused. Not Lawful Good enough to be a Stark, not Chaotic enough to be a Greyjoy, and all I really want to do is go home, but I don't know where that is, and even if it might have been Winterfell in hindsight, oh wait I fucked that up too, didn't I? Why are you asking me this again?