No cause of death was given by the hospital where he died on Thursday. The controversial chess legend had been in hospital since November, when he was treated for a kidney problem.
Fischer had moved to Iceland in 2005 after having lived in Japan in seclusion from the world media for many years. He was a constant and fierce critic of the U.S. government and subsequently gained Icelandic citizenship.
The man who called the 9/11 attacks on the U.S. "wonderful news," first came to public attention in 1972 after beating the Soviet Union's Boris Spassky in a World Championship Match that took place in Reykjavik during one of the tenser periods of the Cold War.
Fischer's victory was a priceless propaganda coup for the U.S., ending decades of international domination of the sport by the U.S.S.R. and turning the new world chess champion into an instant national hero.
In 1992, Fischer and Spassky played a rematch in the former Yugoslavia, under strict UN sanctions at the time. He was later charged with breaking a UN embargo and a warrant was issued for his arrest by U.S. authorities. The game, billed as "Revenge Match of the Century" ended in a second victory for Fischer.
Despite having Jewish parents, Fischer was well-known for his anti-Semitic and anti-Israel views. After the 9/11 attacks on the U.S. he famously said in an interview: "Nobody cares ... [that] the U.S. and Israel have been slaughtering the Palestinians for years," adding that the U.S. would have to be "destroyed" if it failed to change its foreign policy.