Smith played 16 seasons in the National Hockey League (NHL) for the Dallas Stars, Tampa Bay Lightning, Phoenix/Arizona Coyotes, Calgary Flames, and the Edmonton Oilers.

Smith went to play for the Houston Aeros in 2004–05, sharing the net almost equally with Josh Harding, putting up a 0.915 save percentage and 2.42 GAA.

After a faster-than-expected recovery, Smith attended the Dallas Stars' training camp in the fall of 2006, and was awarded the backup goaltender position behind Marty Turco.

In his first-ever regulation NHL game on October 21, 2006, Smith stopped 22 shots to post a shutout against the Phoenix Coyotes.

On February 26, 2008, Smith was traded, along with Jussi Jokinen, Jeff Halpern and a fourth round draft pick in 2009, to the Tampa Bay Lightning in exchange for Brad Richards and Johan Holmqvist.

[11] Smith set the NHL record for the most saves in a regulation shutout victory, as he stopped all 54 shots he faced in a 2–0 win over the Columbus Blue Jackets on April 3, 2012.

[12] However, his record was later surpassed on January 29, 2014, when Ben Scrivens stopped 59 shots in a 3–0 win for the Edmonton Oilers over the San Jose Sharks.

He went on to record an impressive 38 wins in his first season in Phoenix, as the Coyotes qualified for their third consecutive playoff berth, and finished fourth in voting for the Vezina Trophy, awarded to the league's top goaltender.

The Coyotes then faced the eventual Stanley Cup champions Los Angeles Kings in the Western Conference Finals, losing the series 4–1.

Smith scored with 0.1 seconds left in regulation on an empty net during a win against the Detroit Red Wings.

[15] On June 17, 2017, Smith was traded to the Calgary Flames in exchange for goalie Chad Johnson, prospect Brandon Hickey, and a conditional third-round pick in the 2017 NHL Entry Draft.

[17] This made him the 11th active goalie to reach the milestone and tied him with Jeff Hackett for 69th place on the all-time list.

He also won gold at the 2015 world championships as Canada's starting goalie, going 8–0 through the tournament and recording a shutout streak of 190:03 in the medal round (the final three games).