While I haven't gotten to the books yet, a friend and I just spent a late evening going-on early morning watching all the episodes and, dude, holy shit.
So, the only characters whose types I am reasonably certain of are:
Robert Baratheon: EIE
Once an extremely potent warrior, who led the kingdoms in revolt against the Mad King, now just a sad, fat old man. Clearly traumatized by both the rebellion and the loss of his beloved, he uses the office of the king to do whatever the hell he wants: wenching, hunting, drinking... all seemingly to try and recapture some of his former glory and to fill the void in his life.
Very conscious of threats to his reign and is entirely willing to do even the most deplorable shit (like ordering the assassination of a thirteen year old girl and her unborn child) in order to keep his kingdom secure.
Eddard Stark: LSI
Stern, stable, and very, very principled. Operates completely in the open and despises secrecy and the spy-games in the capital. Very loyal and obedient to his friends, is willing to follow orders he knows are going to cause him no end in grief (like splitting up his family and moving to the capital to be Robert's Hand).