Throughout his career, Bégin played for several NHL teams, including the Calgary Flames, Montreal Canadiens, Dallas Stars, Boston Bruins, and Nashville Predators. He was recognized for his defensive contributions, often serving as a reliable penalty killer and energy player. Bégin's resilience was evident throughout his career, overcoming injuries and setbacks to continue playing at the highest level. His dedication to the game earned him respect from teammates, coaches, and fans alike.