U2 "With or Without You"

Despite the fact U2 has sold tens of millions of albums and has a lead singer who is universally loved for his voice and his philanthropic efforts, U2 rarely found success on the Adult Contemporary Chart.  "With or Without You", for example, only managed to peak at #23 in 1987.

The Cranberries - "Dreams"

My brain will always associate "Dreams" from The Cranberries with My So-Called Life.  An episode of the short-lived teen drama that starred a young (and seemingly always depressed) Clare Danes featured this song.