Meech played his junior hockey for the Red Deer Rebels of the Western Hockey League. There, he teamed with future NHL star Dion Phaneuf as the team's top defensive pairing. On June 23, 2002, he was drafted 229th overall in the 7th round of the 2002 NHL Entry Draft. Meech made his NHL debut on December 7, 2006 at Joe Louis Arena, Detroit, Michigan against the St. Louis Blues. He played in 4 NHL games during the 2006–07 NHL season. While playing for the Grand Rapids Griffins of the American Hockey League, Meech was named an All Star after posting 6 goals, and 23 assists in 67 games. Meech was named to the Red Wings final roster during training camp prior to the 2007–08 NHL season. He would have been exposed to waivers had he been sent to the minor leagues, which factored into the team's decision. Also working in Meech's favor for making the roster was Brent Sopel, on a tryout for the Red Wings, had spontaneously signed with the Chicago Blackhawks and Kyle Quincey broke his hand. In 2008, Meech was named "Detroit Red Wings Rookie of the Year" by the Detroit Sports Broadcasters' Association for his play in the 2007–08 season. Based on the system the Red Wings employ, Meech was sometimes used as a left winger. His versatility in playing both forward and defenseman led to extra playing time. Despite not playing the minimum 40 games and not a minute in the playoffs, Meech had his name engraved on the Stanley Cup, due to a successful petition to the NHL by the Detroit Red Wings organization. Meech scored his first career NHL goal with the Detroit Red Wings on December 4, 2008 against Curtis Sanford of the Vancouver Canucks. On September 8, 2010, Meech was placed on waivers by the Red Wings. Unclaimed, Meech was assigned to the Griffins for the duration of the 2010–11 season. Meech signed a two-way contract with the Winnipeg Jets on July 1, 2011. Meech played in only 2 games with the Jets during the 2011–12 season, in a season largely marred by injury. He signed a one-year, two-way contract with the Winnipeg Jets, on July 1, 2012. On July 14, 2013, Meech signed his first contract with a European team as a free agent on a one-year contract with HC Dinamo Minsk of the Kontinental Hockey League. In the 2013–14 season, Meech played in 23 games with Dinamo Minsk, posting 5 assists, before he was mutually released from his contract. He returned to North America and on January 6, 2014, he signed for the remainder of the season to add a veteran presence with the Texas Stars of the AHL. After two seasons with the Stars, Meech embarked on a European return in signing a two-year contract with Swedish club, Malmö Redhawks on May 6, 2015. In the 2015–16 season, Meech added a veteran presence to the Blueline, contributing with 12 points in 37 games before he was sidelined due to injury. Unable to return to full physical health in the off-season, Meech and Malmö opted to end his contract early in order to continue his rehabilitation on July 22, 2016.
