Cash died in hospital in Nashville, Tennessee, his manager said. He had recently suffered a stomach complaint and spent time in hospital.
He became an icon of American country music from the 1950s, with songs such as I Walk the Line and Ring of Fire.
His wife June Carter Cash, with whom he had recorded many songs, died earlier this year.
Cash was regarded as one of the most important figures in country music, in a career that spanned six decades.
He become as famous for his image as an outlaw figure, famous for playing prisons and creating the myth of the Man in Black, his semi-official nickname.
Cash's albums included Folsom Prison Blues, a 1968 live album recorded at a jailhouse concert.
Cash, who sang in a gruff, baritone voice, had hits in the 1960s with Ring of Fire and A Boy Named Sue.
He finished live touring in 1997, but continued recording albums.
Cash became popular with a new audience of music fans with his American Recordings, which covered contemporary artists.
This year, the video for his cover of hard rock band Nine Inch Nails' Hurt received critical acclaim and many nominations at the MTV Video Music Awards last month.
One of the first to pay tribute was Jan Flederus of his European fan club.
He told BBC News 24: "He had a great voice, and was a great inspiration to all country fans.
"He sang about farmers and the working people - and that's what we all do, so the songs are common to all the people in the whole world.
"His music will go on forever, just like Elvis."
Cash was born in Arkansas in 1932, and started writing his own songs at the age of 12, influenced by country songs he heard on the radio.
In 1957 he became the first artist on the influential Sun record label to release a full album, beating Elvis Presley.
In the 1960s his gruelling schedule of over 300 live shows led to him becoming addicted to amphetamines. His drug abuse led to the collapse of his first marriage to wife Vivianne.
But in the mid 60s he met June Carter Cash, one of country's famous Carter family. She co-wrote Ring of Fire, giving him a top ten hit, and the pair married in 1968.
During his career, Cash won 11 Grammy Awards, most recently a
Best Male Country Vocal Performance.