Everybody types him INTJ, I type him ENTJ. He gets his energy from being the center of attention and leading the pack all the time. Even though he claims to hate people, he can't stand to be away from people for too long - he needs to poke them, it's his addiction. Forman is INTJ, they are more patient, fair, respectful.
I dislike the series, because House is not a realistic character. He's an ENTJ jackass, whose screenplay writers equipped with the knowledge of INTJ. But it doesn't work that way in reality. He should make many more mistakes all the time; he already does a lot, though.
In addition, the actor is ISFP, playing his own shadow, which also makes him too cute, compared with how it is usually.
13 is INFJ, Taub is ISFJ, Cuddy is ESFP, Wilson is INFP, Cameron is ISTJ, Chase is ISFP.
The writers/producers of the story think like INTP/ESFJ, and I'm a little bored with their ways of thinking about social groups already (get Death Note as one example). They induce their own biases into the biases of their characters, which are a little different actually. Meaning, their characters like/dislike not the things they do, but the things the writers assume they do. As all writers, here also the main hero ENTJ is a bit too perfect and impossible conglomerate of everything they would personally like in a man. (INFJ writers do that with ENFP characters.) They try to counter-balance with his weaknesses, but are not very convincing.