The Ontario native attended Clarkson University in Potsdam, New York. Following his first year, he was selected 210th overall by the Kings in the 1975 Amateur Draft. During his last year of eligibility in 1976-77, his goals, assists and point totals of 41-67-108 led the ECAC. It appeared that the Kings had been quite astute two years earlier. The hard-working winger was named an NCAA All-American and the ECAC player of the year.
Taylor burst onto the NHL scene with a 22-goal performance in 1977-78. The next year he exploded with 43 goals, and the following season he was teamed with Marcel Dionne and Charlie Simmer on the "Triple Crown Line". This unit was among the best in the league. In addition to being the line's defensive conscience, he was the grinder who fended off the toughest checkers on the opposing team.
In 1980-81, the competitive right winger registered career highs of 47 goals and 112 points. Following the season, he was placed on the NHL Second All-Star Team. His 106 points the following season were a credit to himself and Dionne since they had to do without Simmer for much of the year as the result of a badly broken leg he had suffered late in the previous season.
Between 1983 and 1986, Taylor represented Canada at three World Championships. His best performance was seven points in 10 games in 1986; the low point was a shattered wrist suffered in 1983, an injury that affected him for nearly a year. By the mid-1980s, Taylor was a respected veteran on the team and the natural choice to succeed Terry Ruskowski as captain in 1985-86.
Although his scoring totals dropped during the latter stages of his career, he remained a 20-goal threat and a respected defensive player. Prior to the 1988-89 season, he enthusiastically turned over his captaincy to incoming superstar Wayne Gretzky. The "Great One" drew attention to the Kings franchise and some of its notable stars like Taylor.
On February 5, 1991, he registered his 1,000th point at the Philadelphia Spectrum. Following the season, the soft-spoken winger's involvement in the community was also lauded and in 1990-91 he was presented with both the Bill Masterton and the King Clancy awards.
In his 16th NHL season in 1992-93, Taylor finally reached the Stanley Cup finals, where the Kings lost to the Montreal Canadiens. He played 33 games in 1993-94, then retired after the Kings failed to make the playoffs.
Many remember Taylor best because he was drafted so late and was such a tenacious competitor. He was also a legitimate star who appeared in five NHL All-Star games and finished in the top 10 of the NHL's scoring race three times. His tireless work for the Kings as community/player relations director and with charities such as the Juvenile Diabetes Foundation made him one of the most respected figures in the NHL.
When Taylor left the game, he stood second on L.A.'s all-time goals and points rankings behind his old linemate Marcel Dionne. In 1995 he followed Dionne and Rogie Vachon as the third member of the Kings to have his number retired by the team. He eventually took a position in the Kings' administration and was named the club's vice-president and general manager on April 22, 1997. Just one day after the 2006 NHL Regular season's end Taylor was relieved of his duties with the Kings as general manager on April 19, 2006.