How famous do these musicians have to be? I know lots of professional musicians who play chess (including myself) but none of us are world-famous.
Musicians & Chess

Hmmm...
Well... for the sake of simplicity... they must be on Rate Your Music.
By the way... what do you play?

I think this is an excellent question, Horrorca. I checked to see if Chopin may have played and http://www.uschesstrust.org/WP/?p=1203 says that he did indeed. However, I was unable to confirm this and they do not cite their source. :(
Chess has long been a game of the aristocracy of many European countries and, prior to the 20th century, it was commonplace for Aristocrats to be trained in a musical instrument. It would not surprise me a bit if you found quite a few musical chess players.
Happy Hunting!

I play the piano but I'm mostly a composer. Most of my chess-playing friends are composers too. I do see certain parallels between classical composition and chess.

Horrorca, my man from Mexico City, I got a great answer right here: Wu Tang Clan!!! My source would be http://www.wuchess.com !!! Check it out. Rza loves chess and I am pretty sure the rest of the Wu Tang like chess too. I heard him on EITM on DC101.1FM on the radio one day talking about his love for chess and how he has a chess website and all kind of other crazy things. Peace!
The majority of the players of chess take artistic talents as the music, painting, sculpture And some notable scientists also were playing chess
WCM Úna O Boyle: http://www.myspace.com/unaoboyle & http://homepage.eircom.net/~unaoboyle

Here is my list of musicans who play chess.
Famous musicians who play/played chess include Jean Absil (composer), Jon Anderson (Yes), Paul Badura-Skoda (pianist), Thomas Beecham (conductor), Beethoven, Tony Blackburn (OK singer and disc jockey), Art Blakey (jazz musician), Sir Arthur Bliss, Bono (U2), Sonny Bono (Sonny and Cher), Alex Borodin (Russian composer), Chris Botti (trumpet player), David Bowie, Anthony Braxton (jazz composer), Adolf Brodsky (violinist and composer), Clifford Brown (jazz musician), John Cage (piano composer), Enrico Caruso (opera singer), Pablo Casals (cellist), Feodor Chaliapin (Russian opera singer), Ray Charles, Cher (Sonny and Cher), Chopin, Xavier Cugat (bandleader), Roger Daltry (The Who), Bobby Darin (singer), Dialated Peoples, Neil Diamond, DJ Green Lantern (rapper), Fats Domino, Antonin Dvorak, Bob Dylan, Hanns Eisner (composer), Mischa Elman (violinist), Ferenc Erkel, Adam Faith, Richard “Kinky” Friedman, Dizzy Gillespie (jazz musician), Gerry Goffin (songwriter), Alexander Goldenweiser (pianist), Josh Groban (singer), Daryl Hall (Hall & Oates), Charles Halle (composer), Oscar Hammerstein (musical director), Robert Howard or Dr. Robert (Blow Monkeys), Immortal Technique, Jay-Z (rapper), Jefferson Airplane musical group, Riginald Noel Johnson (composer), Nic Jones (guitarist), Leo Kahn (violinist), Aram Khachaturian, Fritz Kreisler (violinist), Gene Krupa (drummer), John and Lennon (Beatles), Sean Lennon, John Lill (pianist), LL COOL J (rapper), Ludacris (rapper), Phil Lynott (Thin Lizzy), Lorin Maazel (violinist), Madonna, Johnny Marks, Wynton Marsalis (jazz trumpeter), Dean Martin, Felix Mendelssohn, Yehudi Menuhin (violinist), Dominic Miller (guitarist), Joni Mitchell, Moby, Modest Mussorgsky (composer), Graham Nash (Crosby, Stills, and Nash), Nelly (rapper), Willy Nelson (country singer), David Oistrakh (violinist), Yoko Ono, Elaine Paige (singer), Louis Persinger (violinist), Phish, Gregor Piatigorsky (cellist), Sergei Prokofiev (composer), Jason Rebello (keyboard), Helen Reddy, Ruggiero Ricci (violinist), Tim Rice (lyricist), Sviatoslav Richter (pianist), N. Rimsky-Korsakov (composer), Paul Robeson (singer), Moriz Rosenthal (pianist), Leon Rosselson (folk singer), Giocchino Rossini (composer), David Lee Roth, Arthur Rubinstein (pianist), RZA (rapper), Robert Schumann (composer), Ronnie Scott (jazz musician), Artie Shaw (band leader), Dmitri Shostakovich, Frank Sinatra, Grace Slick, Will smith (rapper and actor), Ringo Starr (Beatles), Isaac Stern (violinist), Sticky Fingaz (rapper), Sting, Richard Strauss (composer), Bjorn Ulvaeus (ABBA), Giuseppe Verdi (composer), Heitor Villa-Lobos, West Indian Girl, Paul Whiteman (jazz musician), Rudolf Willmers (pianist), Tadeusz Wronski (violinist), and Wu-Tang Clan (rapper).

I remember Maurice Ashley once did a write up about celebrities who were avid chess fans. I don't remember the band names but some grunge band members showed up at a simul against him or something like that. But he mentioned Will Smith (more of an actor these days) was somewhat accomplished at chess as his hobby.
I think I also read one time that Kasparov at a very early age showed high potential in music, but chose chess over that endeavor.
And of course, there is me. I play chess and I sing a lot in the shower.
Hey guys... I'm working on a list of musicians who also happen(ed) to be chess players.
Do you know of any others? If so I would be very thankful if you could mention them... also a source confirming it would be greatly appreciated.
Peace.