Stanfill attended Cairo High School in Cairo, Georgia, where he was a three-sport star in football, basketball, and track and field. In football, as a senior, he was named the Class AA Lineman of the Year after leading his team to three Region Championships. In basketball, as a senior, he led his team to the state championship and was named the state tournament MVP. In track and field, he added three state discus and one shot put AA titles.
Georgia’s venerable coach Vince Dooley said of Stanfill, "He was everything you’d want in a defensive tackle. He combined speed, size, range, quickness and competitiveness to make him one of the greatest linemen to ever play the game" 
In a 1968 51-0 thumping of the University of Florida, Coach Dooley allowed Stanfill to finish the game at quarterback. The game was in a driving rainstorm and caused some hard feelings on the part of the Gator team. According to Litkenhous  the 8-1-2 Bulldogs were National Champions that season. However, most other polls and formulas awarded the football national championship to Ohio State University.
Selected to the 50th Anniversary All-SEC team (1933–1982). Also selected the SEC Quarter-Century team (1950–74) and All-SEC 25-year team (1961–1985) and 1960s All-SEC team. In 1984 was voted a member of the Georgia Sports Hall of Fame  and was elected to the College Football Hall of Fame in 1998.
He played for the Miami Dolphins from 1969-'76. As the NFL did not officially maintain sack records until 1982, he unofficially led the Dolphins in sacks in 1969 with eight (Still an unofficial team rookie mark that was tied by Lorenzo Bromell in 1998), and picked off 2 passes and returned both for touchdowns. Voted to the 1969 AFL All-Star game. He went to the AFC-NFC Pro Bowl from 1971 through 1974)
In 1970, started on the 10-4 Dolphins and again unofficially led the team with sacks, this time with 6. The Dolphins, although improving, lost in the playoffs. The following season Stanfill was an All-AFC choice and was unofficially third on the team with 6½ sacks. The Dolphins advanced to the Super Bowl losing 24-3 to the Dallas Cowboys.
He was unofficially second on the 17-0 Super Bowl winning Dolphins team with 10 sacks (behind left defensive end Vern Den Herder's 10½) and was voted All-Pro by the Associated Press. He was a consensus All-AFC selection that unofficially led the Dolphins in sacks in 1973 with 18½ and was a consensus All-Pro and All-AFC selection as the 12-2 Dolphins won their second straight Super Bowl. His unofficial 1973 sack total still stands as the team record, although All-Pro Jason Taylor tied that mark in 2002 . On October 7, 1973, Stanfill set the unofficial single-game sack record versus the New York Jets. Two weeks later, teammate Vern Den Herder tied that mark against the Buffalo Bills.
In 1974, he unofficially led an again-tough Dolphin defense in sacks with 10, and was voted 2nd team All-Pro by the NEA and Pro Football Writers Association and was All-AFC for the 4th straight season. In November, versus the Buffalo Bills, Stanfill tied his own (and Den Herder's) unofficial game record for sacks, again recording five.
Injuries hampered Stanfill in 1975 and 1976- both knee and neck injured limited his playing time, and marked the end to Stanfill's post-season honors. Still, he unofficially recorded 6½ sacks in 1975 and 4 in 1976. The mark in 1976 did, however, tie him for the team lead on a struggling 6-8 Dolphin team .
In all, Stanfill unofficially totaled 67½ career sacks, which was the team record until broken by Jason Taylor, who now has 131 career sacks with the club (139.5 overall). He also is unofficially tied for 4th in the Dolphins' playoff record for sacks with 4 (tied with Bob Baumhower). Stanfill was mentioned by Hall of Famer Nick Buoniconti in his induction speech as being an unsung player on the early 1970s Dolphin teams and as being worthy of consideration for the Hall of Fame.
In 2007, he was voted to the All-Time Miami Dolphin team. 
Stanfill lives in Albany, Georgia and is a real estate broker . Featured in a Sports Illustrated article that detailed the injuries to former NFL players. Also featured was Hall of Fame quarterback Johnny Unitas, Earl Campbell, Joe Jacoby, Curt Marsh, Harry Carson, and others. SI reported that Stanfill had three surgeries between August 1993 and January 1996 to fuse four vertebrae in his spine, a problem that started when he jammed his neck during an exhibition game in 1975. According to Stanfill, the surgeries on his spine have caused a neck pain so severe he can't tip his head back, has little use of his left thumb, and considerable loss of hand and arm strength. He also has had surgery to repair a hip condition that was cutting blood flow to the hip bone. Stanfill says he will eventually have to have the other hip surgically repaired as well.