Getting to Yes
A classic example from Getting to Yes, a book that is based on the work of the Harvard Negotiation Project.
From: http://www-personal.umich.edu/~rtanter/getting.html
Consider the story of two men quarreling in a library. One wants the window open and the other wants it closed. They bicker back and forth about how much to leave it open: a crack, halfway, three quarters of the way. No solution satisfies them both. Enter the librarian. She asks why he wants the window open: To get fresh air. She asks the other why he wants it closed: To avoid the draft. After thinking a minute, she opens wide a window in the next room, bringing in fresh air without a draft.
While the parties concentrated on their positions they could not come to a satisfactory solution. When the librarian concentrated on the parties interests and not positions, she was able to offer a much more acceptable solution.