In his NHL career that spanned 18 years, Carpenter played 1,178 games, scoring 320 goals and 408 assists for 728 points.

He was invited to play in the 1985 NHL All-Star game and he also participated in the 1984 and 1987 Canada Cup tournaments as a member of Team USA.

Primarily due to his clashes with head coach Bryan Murray, the Capitals traded Carpenter to the New York Rangers in the deal that sent Mike Ridley and Kelly Miller to Washington during the middle of the 1986–87 NHL season.

He finished the 1986–87 season with the United States team at the 1987 Ice Hockey World Championship tournament in Moscow after the Kings were eliminated in the first round of the 1987 Stanley Cup playoffs.

His son Robert III "Bobo" had a 2-year entry-level contract with the New York Islanders as of 2019 and played two seasons for their AHL affiliate.

In 2016, Carpenter ran the Boston Marathon in three hours and 47 minutes, having taken up training for the event after leaving a job with the Toronto Maple Leafs.