He was born Richard Walter Jenkins in the village of Pontrhydyfen near Port Talbot and grew up in a poor, Welsh-speaking household with many brothers and sisters. He was raised a Presbyterian, but did have a Jewish maternal grandfather. With the assistance of his inspirational schoolmaster, Philip H. Burton (who legally adopted him), he excelled in school productions. It was at this time that he began to develop the distinctive speaking voice that became his hallmark, having been encouraged by Philip (who sidelined as a BBC radio producer) to "lose his Welsh accent". To this day, many aspiring actors study Burton's style of elocution which has been hailed by critics worldwide.

There is a widespread myth (perhaps encouraged or even believed by some members of his stoutly working-class family) that Richard Burton "won a scholarship to Oxford at the age of sixteen" but left after six months. The facts, as recorded by Burton himself in his own autobiography and in Richard and Philip, which he co-wrote, are as follows: At the age of sixteen, he was forced to leave school and find work as a shop assistant. His former teacher, Philip Burton, recognising his talent, adopted him and enabled him to return to school. In 1943, at the age of eighteen, Richard Burton (who had now taken his teacher's surname), was allowed into Exeter College for a term of six months study. This was made possible only because it was wartime and he was an air force cadet.

In 1952, Burton successfully made the transition to a Hollywood star, appearing in My Cousin Rachel opposite Olivia de Havilland. In 1954, he took his most famous radio role, as the narrator in the original production of Dylan Thomas' Under Milk Wood, a role he would reprise in the film version twenty years later.

An insomniac and notoriously heavy drinker, Burton was married five times - twice, consecutively, to Elizabeth Taylor. Burton and Taylor played opposite each other in Mike Nichols's film of the Edward Albee play Who's Afraid of Virginia Woolf?, in which a bitter erudite couple spend the evening trading vicious barbs in front of their horrified and fascinated guests, played by George Segal and Sandy Dennis. The film is reputed to have been similar to Burton and Taylor's real-life marriage. Taylor and Dennis won Oscars for their roles in the movie.

His reputation as drinker may have been well-earned. However, ongoing back pain and a dependence upon pain medications have been suggested as the true cause of his misery.

Burton was banned permanently from BBC productions in 1974 for questioning the sanity of Winston Churchill and others in power during World War II--Burton reported hating them "virulently" for the alleged promise to wipe out all Japanese people on the planet. Ironically, Burton had got along well with Churchill when he met the former Prime Minister at a play in London, and kept a bust of the great wartime leader on his mantlepiece. Burton courted further controversy in 1976 when he wrote a controversial article about his late friend and fellow Welsh thespian Stanley Baker, who had recently died from lung cancer at the age of 49.

Burton's fourth marriage was to Suzy Hunt, ex-wife of motor racing driver James Hunt, (maiden name Suzy Millar, whose father was a judge in Kenya) and his fifth was to Sally Hay, a make-up artist who later became a successful novelist. While married to Sally, he died suddenly of a cerebral hemorrhage at his home in Switzerland, where he is buried. He was only 58 years old. Burton was buried in a red suit, a tribute to his Welsh roots. In fact, his film contracts always contained the clause that he not work on March 1, St David's Day, the national holiday in Wales.

Burton appears in the 2002 List of "100 Great Britons" (sponsored by the BBC and voted for by the public).

Burton is sometimes erroneously referred to as "Sir Richard Burton", perhaps due to the similarity of his assumed name to that of Sir Richard Francis Burton, but unlike the 19th century scholar, he never received a knighthood.