Blondie's - The Tide Is High saw me through my high school years and subsequent high school breakups, so for nostalgic reasons this song sits high on my list of favourite breakup songs for me.
Although I do love the power, sentiment and emotion of Rihanna's Stay; Christina Aguilera and A Great Big World's Say Something and Glen Hansard and Marketa Irglova's duet Falling Slowly.