Bob Corkum played high school hockey at Triton Regional in Massachusetts before enrolling at the University of Maine in 1985-86 where he scored 33 points as a freshman. After scoring to 18 goals and 29 points in 1986-87, Corkum had 14 goals and 32 points in 1987-88. In 1988-89, his senior college season, he scored 17 goals and 48 points. He also helped his school win the Hockey East championship.
Corkum was drafted 47th overall in the 1986 NHL Entry Draft by the Buffalo Sabres. He made his NHL debut on March 16, 1990 against the Toronto Maple Leafs with a goal on his first shot. He played eight NHL games that season and scored two goals. After a full year in the minors, Corkum played 20 NHL games in 1991-92 and scored six points. In 1992-93, he joined the NHL ranks full-time and scored ten points in the 68 games.
On June 24, 1993, the Anaheim Mighty Ducks claimed Corkum in the Expansion Draft. In his first season with his new team, he led the Mighty Ducks with 23 goals and three short-handed goals. In the shortened 1994-95 season, he scored ten goals and 19 points in just 44 games. In 1995-96, Corkum was traded to the Philadelphia Flyers for Chris Herperger and a seventh-round draft pick. In 76 games he had nine goals and 19 points.
On September 30, 1996, the Phoenix Coyotes claimed Corkum in the Waiver Draft where he played for three years before signing as a free agent with the Los Angeles Kings. He played 45 games that year and recorded eleven points. In 2000-01, he was traded to the New Jersey Devils for future considerations. The Devils advanced to the Stanley Cup finals to defend their championship but lost to the Colorado Avalanche.
On July 16, 2001, Corkum signed as a free agent with the Atlanta Thrashers and played in 65 games before joining the Buffalo Sabres the team which originaly drafted him back in 1986.
Corkum went on to play ten games with the Sabres before calling it a career during the off-season.