Then they'd probably look a little like these digital art pieces by deviantArt artist KaiKoa—also known as Cami Sanders. It's a weird crossover for sure, to mix Pokémon and Game of Thrones, but it actually works!
The one above is obviously Charizard, the most fitting Pokemon for House Targaryen. Here it is in full:
Tentacruel, representing house Greyjoy:
Luxray, representing house Lannister:
Sawsbuck, representing House Baratheon:
And finally, Mightyena, representing house Stark:
If there was a house Tully one, I'm betting it would be Magikarp.
(Via Laughing Squid)