Beyond that album, there's a bunch of other songs that have made it onto the show that didn't make it onto that soundtrack (and a couple that did, but are still really good.)
The main point in looking at this cross section of music from the show is it's tone and how that relates to the show itself, particularly when it comes to the character of house. All of the below songs are fairly moody ones - mostly dealing with loss or are otherwise not really 'up' songs. Overall, they form a really good feel for the show and House himself, who is a fairly depressed character all things considered. The comedy in the show aside, there's usually a couple of moments where we really see House as himself - alone and depressed. These songs fit perfectly.
Are You Alright? - Lucinda Williams
Beautiful - Elvis Costello
Colors - Amos Lee
Good Man - Josh Ritter
Grey Room - Damien Rice
Hope for the Hopeless - A Fine Frenzy
Human - Civil Twilight
In The Deep - Bird York
Orange Sky - Alexi Murdoch
See The World - Gomez
Some Devil - Dave Matthews
Walter Reed - Michael Penn