Brian McKnight - "Anytime"

One of 1998's most played songs on the radio wasn't even released as a single.  That song was "Anytime" from Brian McKnight".  Because it was never officially released as a single, the song was ineligible to chart.  Whoops.

Duncan Sheik - "Barely Breathing"

Sometimes it's the song that you throw onto an album as "filler" that goes on to become your breakthrough hit.  In the case of Duncan Sheik, the group added "Barely Breathing" as a throwaway track in order to complete their album.  The song caught fire and went on to be one of 1997's most played songs on the radio.