This may seem kind of irrelevant to people that are later in/have finished the series, but I'm currently on episode 10 of season 3, and thought I'd share my insight on the relationship between Dr House and defective Detective Michael Tritter.
I'm finding these two characters' interaction to be the most interesting in the series yet - not because of clashing personalities, but because of their astounding similarities. Comparing them in terms of motive and how they execute achieving it, they are basically identical.
If you go back an episode or two before Tritter is introduced, House is harassing Cuddy and refusing to use his own office until she replaces his carpet. This probably struck most viewers as odd, given the only difference is an ugly blood stain in the corner. But if you look past the obvious, what House is achieving by making Cuddy cave and replace his carpet is dominance. Power over her.
Then look at Tritter, who is humiliated by House (I won't go into details) who returns, asking for an apology from House. When he doesn't get it, he proceeds to make life harder for House's superiors and subordinates alike, in a second attempt to make House apologise.
I was watching the following episodes, practically shouting at House for not just giving Tritter his trivial request, but then I realised - it doesn't matter how much pain and inconvenience Tritter causes House. He can bend him as much as he wants, but he will never break him. He will never win their underlying psychological battle, because House won't give him power over him by apologising.
The main reason I find this part of the story so interesting, is because it proves that House's will isn't just phenomenally strong; it's indestructible.