Snyder, who also spent five years as UC Berkeley's head football coach, died at his home in Phoenix, the university announced. He had been diagnosed with skin cancer in June.
From 1992 to 2000, Snyder coached at Arizona State. His best season was 1996, when ASU went 11-0 in the regular season but lost to Ohio State in the final seconds of the Rose Bowl. That year, he was named Pac-10 coach of the year.
"He was a guy that helped a lot of us kids grow up, especially myself," said Keith Poole, a wide receiver on that 1996 team. "He taught you how to be tough. He didn't have any soft love. You learned to respect him for that."
Snyder left coaching after he was fired by Arizona State in 2000 after a 6-6 season.
Previously, he had coached football at Cal for five seasons beginning in 1987. He was named 1990 Pac-10 coach of the year after leading Cal to a 7-4-1 record and only its second bowl game since the 1958 season, according to ASU.
His first head coaching job was at Utah State University, from 1976 to 1982.
Bruce Fletcher Snyder was born March 14, 1940, in Santa Monica. He was one of eight children of Lyman and Ida Snyder and grew up moving frequently for his father's contracting business.
At the University of Oregon, Snyder studied mathematics and played football, including starting both as a linebacker and fullback for the 1960 squad that earned a trip to the Liberty Bowl.
Before graduating with a bachelor's degree in 1965, Snyder coached a Little League team and discovered he had an affinity for it. He started out as an assistant football coach at a Eugene, Ore., high school and did the same job from 1964 to 1971 at Oregon University.
At Oregon, he had played for John Robinson, then an assistant coach, and also served with him on the Oregon staff. They coached together at USC in the 1970s and again in the National Football League when Snyder was an assistant coach for the L.A. Rams from 1983 to 1986.
The cancer caused Snyder to struggle with the mind-over-matter philosophy he had preached as a coach, he told the Arizona Republic last fall.
"I'm testing my own toughness about what I used to teach," said Snyder, who kept a blog, http://caringbridge.org/visit /brucesnyder that chronicled his health struggles and optimistic outlook under the headline "Game on!"
Snyder is survived by his wife, three daughters, two grandchildren, four sisters and two brothers.
Services will be private.