As head coach of the Ohio State Buckeyes, Hayes led his teams to a 205-61-10 record (.761), including three national championships (1954, 1957 and 1968), 13 Big Ten conference championships, and four of the team's eight Rose Bowl appearances. Hayes considered the "greatest victory" of his career the 42-21 win over the University of Southern California during the 1974 Rose Bowl. Three-time winner of The College Football Coach of the Year Award, now known as the Paul "Bear" Bryant Award, Hayes was "the subject of more varied and colorful anecdotal material than any other coach past or present, including fabled Knute Rockne," according to biographer Jerry Brondfield.

Hayes' basic coaching philosophy was that "nobody could win football games unless they regarded the game positively and would agree to pay the price that success demands of a team." His conservative style of football (especially on offense) was often described as "three yards and a cloud of dust"—in other words, a "crunching, frontal assault of muscle against muscle, bone upon bone, will against will." The basic, bread-and-butter play in Hayes' playbook was a fullback off-tackle run.

Despite this seeming willingness to avoid change, Hayes became one of the first major college head coaches to recruit African-American players, including Jim Parker, who played both offensive and defensive tackle on Hayes' first national championship team in 1954. While Hayes wasn't the first to recruit African-Americans at Ohio State, he was the first to recruit and start African-Americans in large numbers there and to hire African-American assistant coaches.

Another Hayes' recruit, Archie Griffin, remains the only two-time Heisman Trophy winner in seven decades of selections. Altogether Hayes had 58 players earn All-America accolades under his tutelage, while many notable football coaches, such as Lou Holtz, Bill Arnsparger, Bill Mallory, Dick Crum, Bo Schembechler, Ara Parseghian and Woody's successor, Earle Bruce, served as his assistants at various times.

Hayes would often use illustrations from historical events to make a point in his coaching and teaching. When Hayes was first hired to be the head coach at OSU, he was also made a "full professor of physical education," having earned an M.A. degree in educational administration from Ohio State in 1948. The classes that he taught on campus were usually full, and he was called "Professor Hayes" by students. Hayes also taught mandatory English and vocabulary classes to his freshman football players. One of his students was a basketball player named Bobby Knight, who later became a legendary basketball coach.

During his time at Ohio State, Hayes' relationships with faculty members were particularly good. Even those members of the faculty who believed that the role of intercollegiate athletics was growing out of control respected Hayes personally for his commitment to academics, the standards of integrity with which he ran his program, and the genuine enthusiasm he brought to his hobby as an amateur historian. Hayes often ate lunch or dinner at the university's faculty club, interacting with professors and administrators.

As a coach and an educator, Hayes was one of the first to use the motion picture as a teaching and learning tool. He was also memorable in that he could be seen walking across campus, taking the time to visit with students. When talking to young people, Hayes treated all of them equally and with respect, without regard to race or economic class. This behavior by Hayes was helpful to Ohio State in quelling the violence and damage from anti-war demonstrations that Ohio State and other college campuses suffered in the late 1960s/early 1970s. He would actually take the time to communicate with student leaders. Said then team quarterback Rex Kern, "Woody was out there on the Oval with the protesters, and he'd grab a bullhorn and tell the students to express their beliefs but not be destructive. He believed in Nixon, and he believed in the Establishment, but he wasn't afraid to talk to the students. He wanted to stay close to the action."[3] Hayes was considered one of the few authority figures that students then had respect for. His enthusiasm for coaching and winning was such that many across the nation consider the following maxim to be true: "What Vince Lombardi was to professional football, Woody Hayes was to college football."

During his tenure at Ohio State, Hayes would joke that he considered himself to be Notre Dame's best recruiter because if he couldn't convince a recruit to come to Ohio State instead of Michigan he'd try to steer the recruit to Notre Dame, who Ohio State didn't play. While Hayes' public stance was that he refused to play Notre Dame because he was afraid of polarizing the Catholic population in Ohio, however, Notre Dame's long-time athletic director Fr. Edmund P. Joyce said that Hayes had told him that Hayes liked having Michigan as the only tough game on the Ohio State schedule and that having the Buckeyes play Notre Dame would detract from that.[4]