One of these Knights (One of these crazy, lonely knights) - The Eagles
Hitting the Right Note (Chess-themed Songs)

Pawn to be Wild (Theme from Easy Rider) - Steppenwolf

Killer Queen by Queen
Black Queen by Crosby Stills Nash and Young
Only a pawn in their game by Bob Dylan
And my personal fav
Knight Moves by Bob Seger and the Silver Bullet Band

Jail house rook- by Elvis, or rook around the clock by Bill Haley and the comets
The King of Rook & Roll - there's a chess player for you.
And a song about chess clocks - for seconds.

from the days before Dylan could play melodies - or perhaps he never could?
- http://www.youtube.com/watch?v=XUvQzgxTxmE

... because you always get to play both colours?

Won't Get Fooled Again - The Who
(http://www.youtube.com/watch?v=NIHJ9RMAVGI)
Not chess-specific, but a valuable sentiment to bear in mind as part of a chess-improvement-programme.

"I've Seen All Good People" - Yes
How about Chess Records? It's not a song but it was a nice recording company.

Then your playing experience here on chess.com has been fortunate.
They turned up in this thread ... http://www.chess.com/forum/view/off-topic/it-was-forty-years-ago-todat-beatles-rooftop-concert
Songs on the theme of chess?