Perhaps the greatest chess player that ever lived, Bobby Fischer was definitely the most famous and is forever entwined with the history of the Cold War. Rather than rehash his life here, I would just say that there's a great movie from about 10 years back called Searching For Bobby Fischer, starring Joe Montegna, Joan Allen, Ben Kingsley and Laurence Fishburne you may want to check out. Despite the title, the movie is not so much about Fischer but about a young chess player's rise in the chess world that still lives in the shadow of Fischer who at the time was in seclusion. Babe Ruth, Baseball...Michael Jordan, Basketball...Bobby Fischer, Chess. That's the bottom line.
Sadly, he was quite mad and it only got worse with age: rabid anti-Semitism and anti-Americanism, but his skills were never in doubt. Only Gary Kasparov has come close...and ironically, he also is involved in international affairs.