What complications should be expected when an unmarried couple's relationship fails after they have purchased a house together? How does this situation compare to that of a married couple?
Generally it depends greatly on the jurisdiction. I'll answer assuming you're in the US (other people tend not to assume that their country is the only one in the world):
For unmarried couples its much less complicated: what's in the title/deed - that's what you get.
For married couples, the state laws regarding community property come into effect (it may also make you "married" for state law purposes, if the relationships were long enough). In this case you need to talk to a family law lawyer.