Dampier was a two-sport athlete at the University of Kentucky, playing baseball as well as basketball. Playing under the legendary coach Adolph Rupp, Dampier, Tommy Kron and Pat Riley led Rupp's Runts to the 1966 NCAA championship game, where they lost to Texas Western College in a watershed game for college basketball. This game spearheaded the end of racial segregation in college basketball. During his three years at Kentucky, Dampier was a two-time All-American and three-time All-Southeastern Conference selection. He was also named Academic All-SEC twice and Academic All-American once. Upon graduation from Kentucky in 1967, Dampier scored 1,575 points, at the time third-most in school history behind only Cotton Nash and Alex Groza.
Pro basketball
In 1967 the Cincinnati Royals selected Dampier in the fourth round of the NBA Draft and the Kentucky Colonels selected him in the ABA draft. Dampier eventually signed with the Kentucky Colonels of the fledgling ABA and teamed with Darel Carrier to form the most explosive backcourt duo in the league. In each of the ABA's first three seasons, both Dampier and Carrier averaged at least 20 points per game. Both were three-point field goal specialists, but especially Dampier who made 500 during a three-year stretch: a record 199 during the 1968–69 season, 198 in 1969–70 and 103 in 1970–71. At the conclusion of the ABA's history, Dampier made a career-record 794 3-point field goals. He also finished first all-time in the ABA in games played, minutes played, points scored, and assists. During the 1970–71 season, he hit 57 consecutive free throws for what was then a pro record. Seven times, he was named an ABA All-Star. He was a unanimous choice for the ABA Top 30 team. He played on the Colonels' 1975 ABA championship team, which featured a later Kentucky standout, Dan Issel, as well as 7'2" center Artis Gilmore. After the 1976 season, the ABA ceased operations with Kentucky and two other teams folding. Dampier was selected by the San Antonio Spurs in the 1976 ABA Dispersal Draft. Playing mostly as a role player behind George Gervin, Dampier averaged 6.7 points in 232 NBA games. Dampier later served as an assistant coach with the Denver Nuggets. Several divisions in the 21st century semi-pro ABA were initially named after stars of the old ABA, including Dampier. Dampier was inducted into the Naismith Memorial Basketball Hall of Fame in September 2015.