In the beginning, I've thought Tyrion Lannister is an INTP, but he's rather ENTP. He also has a slight ENFP vibe.
HOUSE LANNISTER
Tywin: INTJ
Cersei: INTJ
Jaime: ESTP
Tyrion: ENTP
Lancel: ISTJ
(The "Baratheons")
Joffrey: ENTJ
Myrcella: ISFP
Tommen: ISFP
HOUSE STARK
Eddard: ISFJ
Catelyn: ISTJ
Robb: ESTJ
Jon Snow: INFP
Sansa: ISFJ
Arya: INTJ (yes, Ni, Te, Fi, Se fits her perfectly)
Bran: ISTP
Rickon: Too young to type
HOUSE BARATHEON
Robert: ESTP
Renly: ENFP
Stannis the Mannis: ISTJ
Gendry: ESTP
HOUSE TARGARYEN
Danaerys: INFJ
Viserys: ESTJ
Aemon: INFJ
HOUSE TYRELL
Olenna: ENTJ
Margaery: ENFJ
Loras Tyrell: ESTP
OTHER
Petyr "Littlefinger" Baelish: ENTJ
Lord Varys: As INTJ as it gets
Jorah Mormont: ISFP
Sandor "The Hound" Clegane: ISTP
Gregor "The Mountain" Clegane: ESTP
Samwell Tarly: INFJ
Ygritte: ENTJ
I'll just take this one, as it's the most complete list I've seen this far, and change what I don't agree with.
Tywin, ENTJ, ESTJ before INTJ, but ENTJ nonetheless.
Cersei, probably some Se/Fi. xSFP.
Ned, ISTJ
Jon Snow, ISFP. No Ne, tons of Se.
Arya, ISTP, possibly ESTP. Too reckless to be an INTJ.
I've seen arguments for Stannis being an ISTP, which I can buy. Can agree on ISTJ as well though, as well as ESTJ in the show.
Dany, ISFP. Where is her Ni?
Varys, INFJ. There's no Te in that one, though loads of Fe.
Ygritte would be some ESxP.
Khal Drogo, ESTx.
What about the former Targaryens?
The conquering siblings, Aegon, Visenya and Rhaenys? Rhaegar? Bloodraven?