The Colorado Avalanche selected Parrish as the 79th overall pick in the 1996 NHL entry draught. When he was chosen by the Florida Panthers in 1998, Parrish made his NHL debut. From 1998 to 2000, he was a member of the Florida Panthers. During this time, he appeared in 154 games, scoring 50 goals and amassing 81 points.
He was dealt with the New York Islanders in 2000. From 2000 through 2006, he was a member of the New York Islanders, where he played right wing. During his time with the Islanders, Parrish appeared in 345 games and scored 118 goals. Similarly, he earned a total of 214 points.
Parrish transferred to the Minnesota Wild in 2006 and stayed with them for two years. During his time with them, he appeared in 142 games and scored 35 goals. Similarly, he gained 69 points.
He was traded to the Dallas Stars in 2008. He only played 44 games for the Dallas Stars and scored 8 goals for a total of 13 points. Furthermore, the next year, Parrish transferred to the Tampa Bay Lightning, where he appeared in 16 games and earned two points.
Parrish was a member of the Buffalo Sabres for the 2010/2011 season, but only appeared in two games before retiring the following year.
Parrish had a good NHL career that lasted 12 years. During his career, he appeared in 722 games, scored 216 goals, and totaled 387 points.
