Responding to Xander and Aeth.
If you think House is INTJ you don't fully understand introversion and extraveraion.
Its as simple as that.
Apparently I'd misunderstood how Ne worked, and I'd therefore changed my opinion to INTP. However, that still makes my guess an introvert, but that's more based on my opinion of his function order rather than the whole introversion/extroversion thing. I stand by my earlier statement that in terms of introversion/extroversion, he's probably somewhere close to the dividing line and that my guess is he's an introvert due to the way he constantly pushes people away and likes spending time alone. I do realize that it's possible for someone to be raised in the conditions that he was raised in and as a result are suppressed extroverts, though in my opinion the reason he seems extroverted is due to his auxiliary trait being highly developped (which it is either way).
My initial reasoning for him being INTP was that he only seems to bring out his Ne during cases (or when he's randomly analysing his staff), but not all the time, whereas he's always interested in logical analysis. After looking into it more, there seems to be furthur evidence to support it. Earlier I'd stated that he acted under a moral code (which was my case for Fi), but now I believe him to act under a code of principals which is derived from dominant Ti. Also, he becomes interested in cases due to logical discrepensies (a result of Ti), after which Ne comes into play.
I also find it interesting that the more stressed he get, the more outwardly emotional he gets. This particularly happens when his Vicodin is taken away, though I'm not sure whether or not drug withdrawal should be considered in his functional analysis. Either way, under stress he resorts to yelling, attempting to wound others emotionally and being generally irrational, which could be seen as the result of an unhealthy Fe shadow. However, here's where my oh-so-pretty analysing breaks down, as I'm not entirely clear on what an Si-dominant shadow would look like, so I can't make that comparison.
Anyways,
here's where I've been getting most of my information if you're curious about my sources. Feel free to randomly pick apart and destroy any of my points.