He first appeared on television in series such as Marcus Welby, M.D. (1969), Wonder Woman (1975), Laverne & Shirley (1976) and Angie (1979). He made his feature-film debut in the landmark comedy Airplane! (1980), starring as Ted Striker, the traumatized former pilot who must land the plane when the flight crew gets struck by food poisoning. He later reprised his role as Ted Striker in Airplane II: The Sequel (1982).

After the massive success of Airplane!, Hays went on to star in many feature films including Take This Job and Shove It (1981), Trenchcoat (1983), Cat's Eye (1985), Fifty/Fifty (1992), Homeward Bound: The Incredible Journey (1993), Homeward Bound II: Lost in San Francisco (1996), Robert Altman's Dr. T & the Women (2000) and Alex in Wonder (2001), which he also produced. He starred in over 20 made-for-TV movies like NBC's Mister Roberts (1984), CBS' Murder by the Book (1987), and Lifetime's The Abduction (1996). He also had a surprise appearance in Sharknado 2: The Second One (2014). Hays also had numerous guest appearances on various television shows including Touched by an Angel (1994), Promised Land (1996) and That '70s Show (1998), and he starred in the series Starman (1986), FM (1989), Cutters (1993) and Kelly Kelly (1998).