Born in Ashwood, Virginia, near Hot Springs, Snead began caddying at age seven at The Homestead in Hot Springs. He worked as an assistant pro at The Homestead at 19 and turned professional in 1934. Snead joined the PGA Tour in 1936, and achieved immediate success by winning the West Virginia Closed Pro tournament.

In 1936, Snead won his first tournament, the West Virginia Closed Pro, contested at The Greenbrier's Championship Course and Old White Course. He shot rounds of 70-61 to rout Logan, West Virginia, pro Clem Weichman by 16 strokes (74-73). Later that summer, he won the first of 17 West Virginia Open championships by beating Art Clark by five strokes at Guyan Country Club in Huntington, West Virginia.

He played on seven Ryder Cup teams: 1937, 1947, 1949, 1951, 1953, 1955, and 1959. He captained the team in 1951, 1959, and 1969.

Snead won the Vardon Trophy, for lowest scoring average, four times: 1938, 1949, 1950, and 1955.

The year 1939 was the first of several times where Snead failed at crucial moments of the U.S. Open, the only major event he never won. Needing par to win, but not knowing that, since on-course scoreboards did not exist at that time, Snead posted a triple-bogey 8 on the par-5 72nd hole. Snead had been told on the 18th tee by a spectator that he needed a birdie to win.

Snead served in the U.S. Navy during World War II from 1942 to 1944. He was an athletic specialist in Cmdr. Gene Tunney's program in San Diego, and was given a medical discharge for a back injury in September 1944.

At the U.S. Open in 1947, Snead missed a 30-inch (76 cm) putt on the final playoff hole to lose to Lew Worsham.

In 1950, he won 11 events, placing him third in that category behind Byron Nelson (18, in 1945) and Ben Hogan (13, in 1946). His scoring average of 69.23 was a Vardon Trophy record that stood for 50 years until broken by Tiger Woods in 2000.

At the 1952 Jacksonville Open, Snead forfeited rather than play an 18-hole playoff against Doug Ford after the two golfers finished in a tie at the end of regulation play. The forfeit stemmed from a ruling Snead received during the tournament's second round of play. On the 10th hole, Snead's drive landed behind an out of bounds stake. While Chick Harbert, who was playing with Snead, thought the ball was out of bounds, a rules official ruled differently due to the starter not telling players the stakes had been moved after the previous day's play had ended. Afterwards, Snead explained why he forfeited even though Ford suggested they play sudden death for the title. "I want to be fair about it. I don't want anyone to think I took advantage of the ruling."

Note: The PGA Championship was match play until 1958.
Defeated Ben Hogan in 18-hole playoff – Snead 70 (−2), Hogan 71 (−1)

In December 1959, Snead took part in a controversial match against Mason Rudolph, at the Mid Ocean Club in Bermuda. Snead decided to deliberately lose the televised match, played under the "World Championship Golf" series, during its final holes, after he discovered on the 12th hole that he had too many golf clubs in his bag. (A player is limited to 14 clubs during competitive rounds.) The match was tied at that stage. The extra club in his bag, a fairway wood Snead had been experimenting with in practice, would have caused him to be immediately disqualified according to the Rules of Golf, even though he did not use it during the round. After the match was over, Snead explained the matter, and said he did not disqualify himself in order not to spoil the show. The Problem did not become known outside a small circle until the show was televised four months later. After the incident came to light, the sponsor cancelled further participation in the series.

During his peak years, Snead was an exceptionally long driver, particularly into the wind, with very good accuracy as well. He was a superb player with the long irons. Snead was also known for a very creative short game, pioneering use of the sand wedge for short shots from grass. As he aged, he began to experiment with different putting styles. Snead pioneered croquet-style putting in the 1960s, where he straddled the ball with one leg on each side. The United States Golf Association banned this technique in 1968 by amending the old Rule 35–1, since until that time, golfers had always faced the ball when striking. Snead then went to side-saddle putting, where he crouched and angled his feet towards the hole, and held the club with a split grip. He used that style for the rest of his career.

Snead wrote several golf instructional books, and frequently wrote instructional columns in golf magazines. His 1962 autobiography was titled The Education of a Golfer.

In 1971, he won the PGA Club Professional Championship at Pinehurst Resort.

In 1973, Snead became the oldest player to make a cut in a U.S. Open at age 61.

He shot a final round 68 at the 1974 PGA Championship to finish tied for third, three strokes behind winner Lee Trevino. At age 62, it was Snead's third consecutive top-10 finish at the PGA Championship, but his last time in contention at a major.

In 1978, he won the first Legends of Golf event, which was the impetus for the creation, two years later, of the Senior PGA Tour, now the Champions Tour.

In 1979, he was the youngest PGA Tour Golfer to shoot his age (67) in the second round of the 1979 Quad Cities Open. He shot under his age (66) in the final round.

In 1983, at age 71, he shot a round of 60 (12-under-par) at The Homestead in Hot Springs, Virginia.

From 1984 to 2002, he hit the honorary starting tee shot at The Masters. Until 1999, he was joined by Gene Sarazen, and until 2001, by Byron Nelson.

In 1997, at age 85, he shot a round of 78 at the Old White course of The Greenbrier in White Sulphur Springs, West Virginia.

In 1998, he received the PGA Tour Lifetime Achievement Award, the fourth person to be so honored.

In 2000, Snead was ranked the third greatest Golfer of all time, in Golf Digest magazine's rankings, behind only Jack Nicklaus and Ben Hogan.

Snead died in Hot Springs, Virginia, in 2002 following complications from a stroke, four days before his 90th birthday. He was survived by two sons: Sam Jr. of Hot Springs, and Terry, of Mountain Grove, Virginia, and a brother, Pete, of Pittsburgh, as well as two grandchildren. His wife Audrey died in 1990. His nephew J. C. Snead was also a PGA Tour Golfer.

Snead held the record for most PGA Tour wins after reaching age 40, with 17, until the record was broken at the 2007 Mercedes-Benz Championship by Vijay Singh.

In 2009, Snead was inducted into the West Virginia Golf Hall of Fame.