This is kind of a tough one. I mean the easy answers, and the most popular, would be House Stark or House Targaryen. I like both of those houses, and really I like all the houses cause I am the biggest Game of Thrones nerd you know. However, When I answer this question I always think about who are the most interesting characters of A Song of Ice and Fire? When you think about it like that the choice becomes clear, even though it will be very unpopular. Therefore I decree that my fave house is House Lannister of Casterly Rock.
I mean I already confessed that Tyrion Lannister is my favorite character. I think those of us who have read all the books thus far have a deeper understanding of the struggles of Jamie Lannister. Cersei is a total bitch but damn are her chapters fun to read. Tywin is the ultiamte bad ass, and he may suck at parenting but damn is he the last guy to mess with. Lancel sucks, and so does his dad really. And let us not forget the guy we all love to hate that miserable little prick Joffrey. Put come on in a world where we route for the bad guys kind of a lot (Tony Soprano, and Jax Teller come to mind) why not enjoy the dysfunction that is the Lannisters.
I guess the one draw back here is while they were bringing about the fall of House Stark, thanks to Joffrey, they get completely out maneuvered by House Tyrell and we learn who plays the Game of Thrones the best. That really crazy old bitch who might become all of our's favorite if she continues to be awesome on the TV show. Queen of Thorns is a heck of a nickname and even a thorn can bring down a lion.
House Lannister is my favorite because of Tyrion, and Tywin, and Jamie. They have my favorite characters and really they have the most hated characters. That is a very interesting dynamic to me and it is very entertaining. At the end of the day that is what it is all about.