"Hunter prized his privacy and we ask that his friends and admirers respect that privacy as well as that of his family," Juan Thompson said in a statement.
Pitkin County Sheriff Bob Braudis, a personal friend of Thompson, confirmed the death.
Juan Thompson found his father's body. Thompson's wife, Anita, was not home at the time.
Besides the 1972 drug-hazed classic about Thompson's visit to Las Vegas, he also wrote Fear and Loathing: On the Campaign Trail '72. The central character in the wild, sprawling satires was Dr Thompson, a snarling, drug and alcohol-crazed observer and participant.
Thompson is credited with pioneering New Journalism or, as he dubbed it, "gonzo journalism" in which the writer made himself an essential component of the story. Much of his earliest work appeared in Rolling Stone magazine.
"Fiction is based on reality unless you're a fairy-tale artist," Thompson said in 2003. "You have to get your knowledge of life from somewhere. You have to know the material you're writing about before you alter it."
An acute observer of the decadence and depravity in American life, Thompson also wrote such collections as Generation of Swine and Songs of the Doomed. His first ever novel, The Rum Diary, written in 1959, was published in 1998.
Thompson was a counterculture icon at the height of the Watergate era, and Richard Nixon once said he represented "that dark, venal, and incurably violent side of the American character."
Thompson also was the model for Gary Trudeau's balding Uncle Duke in the comic strip Doonesbury and was portrayed on screen by Johnny Depp in a film adaptation of Fear and Loathing in Las Vegas.
Other books include The Great Shark Hunt, Hell's Angels and The Proud Highway. His most recent effort was Hey Rube: Blood Sport, the Bush Doctrine, and the Downward Spiral of Dumbness.
His compound in Woody Creek, not far from Aspen, was almost as legendary as Thompson. He prized peacocks and weapons; in 2000, he accidentally shot and slightly wounded his assistant, Deborah Fuller, trying to chase a bear off his property.
Born July 18, 1937, in Kentucky, Hunter Stocton Thompson served two years in the Air Force, where he was a newspaper sports editor. He later became a proud member of the
National Rifle Association and was almost elected sheriff in Aspen in 1970 under the Freak Power Party banner.
Thompson's heyday came in the 1970s, when his larger-than-life persona was gobbled up by magazines.
His pieces were of legendary length and so was his appetite for adventure and trouble; his purported fights with Rolling Stone editor Jann Wenner were rumoured to hinge on expense accounts for stories that didn't materialise.
His book on the 1972 presidential campaign involving Edmund Muskie, Hubert Humphrey and Nixon, was famous for its scathing opinion.