Before I put my point of view here, I should admit a few things:
I am a doctor.
Colleagues often comment on how I startle them by 1. remembering unusual patterns and case studies in medicine 2. coming up with plausible diagnoses that they hadn't considered, because they look for horses but I'm aware that just occasionally the guy down the road decided to import a zebra.
I'm an INTJ, so naturally I'm going to argue for my own type.
House is an INTJ who has been partially socialised by his training.
Most of you are tending to the 'INTJs don't need anyone' argument, forgetting that actually INTJs do, they just have 10ft thick walls around them which makes it look as though they don't.
To become a consultant in a major western hospital you have to teach, so much so that those of us who would generally avoid that sort of interaction become first desensitised to it, and then (sometimes) start to require it. It is also one of the few rewards for the logical mind - an audience of almost-peers agreeing that your deductions were correct. INTJs like to be recognised as right by those who have a similar knowledge base. In House's case another doctor at his level would work in another specialty, ie not have the same area of expertise, and so any recognition from them would be of no value. His juniors are heading towards his knowledge base, so he does get something from them as an audience. He has consequently acquired a set of behaviours associated with coming up with a diagnosis which actually involves a significant degree of performance to an audience. He will therefore start to perform to those who are not his peers, because he's actually well inside his own head, and by now the audience can be anybody.
His friendship with Wilson is classic, too. Wilson, though often temporarily hurt by things House says, has the ability to look past them to the underlying human being. He knows House likes him; he knows House would bite his tongue out rather than say the words. House's behaviour in concealing the answering machine message and making Wilson stay on in his flat is typical INTJ 'I'll do what I think is best for you no matter what you may feel about it' behaviour. Where their friendship staggers is when House's need to do what he knows is right clashes with his loyalty to Wilson. Right wins out; Wilson knows it always will, and this is the one permanent crack in an otherwise solid friendship. This is the point on which Wilson has to give if their friendship is to survive. On the other hand, there is enough trust on House's part for him to let Wilson see that he can and does empathise with the distress he's caused. Though perhaps most sensors might find that too subtle and insist that 'he doesn't care' when in fact he cares too much - these are the situations where INTJs become so distressed that they can withdraw completely and become quite dissociated from reality.
House follows his own book - it's a deeply logical thought process, trying to match symptoms and signs to an underlying pathology. It's Holmes, as always - 'whatever you're left with, however implausible, must be the truth.' He doesn't use other people's books/thought pathways/logic, because these have clearly failed. He may be using what look like intuitive leaps (I was once told that my thinking was so lateral I'd lateraled myself out of the window) but in fact it's simply a mix of logic and statistics (also known as experience), combined with deep expertise and a willingness to look for things that are very unusual.
INTJs also indulge in solitary sensory experiences, be it standing in a shower for hours or riding at speed on a motorbike. It's the rare time in which they let their thought processes idle and give free rein to the feelings of the moment.
He also left a woman because she did something she'd promised not to. He knows she did the right thing, but she broke a promise. He can't trust her any more.
INTJ.