Quincey, a defenseman, joined his seventh NHL team when he signed a one-year contract by the Minnesota Wild on July 1, 2017. The native of Kitchener, Ontario, had three assists in 18 games with the Wild. He previously played with the Detroit Red Wings, Los Angeles Kings, Colorado Avalanche, Tampa Bay Lightning, New Jersey Devils and Columbus Blue Jackets after the Red Wings chose him in the fourth round (No. 132) of the 2003 NHL Draft.

Quincey grew up in Caledon, Ontario, playing most of his minor hockey for the Halton AAA program of the OMHA before he was taken by London in the third round (No. 47) of the 2001 Ontario Hockey League Priority Selection. After a trade to Mississauga at the start of the 2003-04 season, Quincey helped the IceDogs to the OHL Final, where they were swept in four games by Guelph.

The following season, Quincey had OHL career highs of 15 goals, 31 assists and 46 points in 59 games. He was named to the OHL Second All-Star Team, and finished third in voting for the Max Kaminsky Trophy, given to the league's top defenseman.

Quincey signed a three-year contract with the Red Wings on July 28, 2005, but spent most of his time with Grand Rapids of the American Hockey League, finishing fifth among rookie AHL defensemen with 33 points (seven goals, 26 points) in 70 games. He made his NHL debut against the Mighty Ducks of Anaheim on Nov. 25, 2005.

The following season, Quincey was a late call-up to the Red Wings and appeared in 13 Stanley Cup Playoff games because of injuries to defensemen Niklas Kronwall and Mathieu Schneider. He was on track to parlay that experience into a regular roster spot in Detroit, but broke his hand in training camp and missed the 2007-08 preseason. He was on the practice roster for the Red Wings team that won the Stanley Cup in 2008.

Quincey was claimed off waivers by the Kings on Oct. 13, 2008, and went on to lead Kings defensemen with 34 assists and 38 points in 74 games before a herniated disk ended his season on April 1, 2009. He spent the next three seasons with the Avalanche before he was traded to the Lightning on Feb. 21, 2012, and, moments later, sent back to the Red Wings.

In 2013-14, Quincey was one of two Red Wings to play in all 82 games, and he signed a two-year contract to stay in Detroit.

On Sept. 28, 2016, Quincey signed one-year contract with the New Jersey Devils but was traded to the Columbus Blue Jackets on March 1, 2017.