There's the musical Chess, which is very good. The plot centers around Cold War politics, so some of it may seem dated.
Songs About Chess
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http://www.youtube.com/watch?v=TgmoEHnUpjk&feature=related
One night in Bangkok from the musical Chess.
i think john mayer has a song where he talks about playing chess with salt and pepper shakers? ah, found it. "I played a quick game of chess with the salt and pepper shakers" :)
http://www.youtube.com/watch?v=ic0FCyZUo1E
What does the Abba video have to do with chess?
Who cares, it's Abba baby!
WOOHOO
She is the dancing QUEEN!
I'm not crazy about rap music, but this song's got a groove and gives chess the hip aura it deserves...(also dig the Kasparov lecture samples floating in the background 
)
http://www.youtube.com/watch?v=WPEf-DFKHRQ&feature=related
One Night in Bangkok is a chess song, look up the lyrics ... plus it's awesome.
"Only a Pawn in Their Game" by Bob Dylan. That's more of a chess metaphor than actually about chess. http://www.bobdylan.com/#/songs/only-pawn-their-game BTW, I loved One Night in Bangkok when they performed it in Chess, the Musical on PBS.
haha i was about to write a post on the topic when i came across this one.
the GZA has a whole album dedicated to chess called Grandmasters with song titles such as, Smothered Mate, Destruction of a Gaurd, Unprotected Pieces etc.
also, i like the opening line of Red Hot Chilli Pepper's Fortune Faded
Half Man, Half Biscuit (I've been plugging them a bit!) have one:
http://www.chrisrand.com/hmhb/csi-ambleside/bad-losers-on-yahoo-chess/
Think they have some references in other songs too
HA... Judging from the song titles, most of that GZA album is chess related... interesting.
"THE BALLAD OF BOBBY FISCHER
By DAVID L. AMKRAUT, USCF Expert
"THE BALLAD OF BOBBY FISCHER," (record) sung by Joe Glazer and the Fianchettoed Bishops. Available from Collector Records, Suite 209, 8422 Georgia Avenue, Silver Spring, MD 20910.
In addition to everything else, Bobby is now being idolized in song.
Sung in twangy, country-music style by Joe Glazer and the Fianchettoed Bishops, the seven-minute "Ballad of Bobby Fischer" relates Bobby's career from the beginning ("He opened his mouth on the day he was born... and said move that pawn") through his school days ("Sittin' in the classroom he barely could think, 'cause chess was his food, chess was his drink") on through the Interzonal and the Candidates Matches ("Despite his attempts to innovate Larsen was bent right out of shape") and concludes with Bobby Fischer Champion of the World and a disgraced Boris Spassky being hustled off to Siberia."
I have on hand a British chess mag from the time that has all the lyrics.
The Arcade Fire song, "Deep Blue," mentions the 1996 match in which IBM's Deep Blue was defeated by Kasparov. Also, it's an awesome song.
Are we forgetting "Like a g6" by Far east movement
That song is always in my head as black begins to fianchetto :P
Bob Segar taught me how the knight moves.
But Suzanne Vega actually has a song named Kinght Moves.
http://www.youtube.com/watch?v=zqIclJjrCgU
Watch while the queen
In one false move
Turns herself into a pawn
Weezer has a song called "Chess" and its the only song that I know of that is about chess and they use it as a metaphor for relationships. You can check out the lyrics here: http://www.lyrics007.com/Weezer%20Lyrics/Chess%20Lyrics.html
The Weezer song is pretty good too. I like it.
Are there any other bands that have written songs using chess as the main subject of thier lyrics?