Richardson has also played for the Edmonton Oilers, Philadelphia Flyers, Columbus Blue Jackets, Tampa Bay Lightning, and Ottawa Senators.

Richardson was selected seventh overall by the Toronto Maple Leafs in the 1987 NHL entry draft after two successful seasons with the Peterborough Petes of the Ontario Hockey League (OHL).

Midway through his rookie NHL season, on January 6, 1988, Richardson was the victim of an infamous attack from Dino Ciccarelli of the Minnesota North Stars, who clubbed him over the head several times with his stick.

He remained a regular on the Toronto blueline until 1991 when he was involved in a blockbuster trade, moving to the Edmonton Oilers (along with Vincent Damphousse, Scott Thornton, Peter Ing, future considerations and cash) in exchange for Grant Fuhr, Glenn Anderson and Craig Berube.

On August 7, 2007, Richardson signed a one-year, $500,000 two-way contract with his hometown Ottawa Senators, amid the speculation he would soon announce his retirement from the NHL.

On February 15, 2008, Richardson was named the Senators' nominee for the Bill Masterton Memorial Trophy, though the award went to Jason Blake of the Toronto Maple Leafs.

During his rookie season as head coach, Richardson led an inexperienced Binghamton team to a 44–24–1–7 record, finishing fourth in the AHL's Eastern Conference.

[7] With Ducharme participating virtually, Richardson led the team to win the series and move forward to the 2021 Stanley Cup Finals.

[9] Despite a challenging first two seasons as head coach in which the team went a combined 49–102–13, Richardson was praised for his managerial abilities despite working with a weak roster.

[13] Before he started his NHL career, Richardson played for Canada national junior team in 1987 and was involved in the infamous Punch-up in Piestany brawl.