220px-Norah_Jones_-_Come_Away_With_MeNorah Jones – “Come Away With Me” – (2002)

Remember after 9/11 when Norah Jones swooped in and swept America off its feet? Though not a pop smash, this song (the title track from her debut album) is one the jazziest songs to receive any kind of mainstream radio airplay in the last quarter century. Songs like this is why this album won Album of the Year at the Grammys.