Brewer was born on April 17, 1979, in Vernon, British Columbia, to Anna and Frank Brewer. He was raised in Ashcroft, British Columbia, and began playing ice hockey in the Ashcroft Minor Hockey program. When he was fourteen, his family moved to Kamloops, British Columbia, where he attended junior and senior high school. Brewer excelled with the Kamloops Bantam AAA Jardine Blazers of the British Columbia Amateur Hockey Association (BCAHA). In 1995, Brewer was exposed to BCAHA Best Ever, a program designed to find and develop players and coaches for play in international competition. As a young hockey player, Brewer looked up to NHL stars Scott Niedermayer and Jeremy Roenick as role Models.

Brewer was drafted in the sixth round, 81st overall, by the Prince George Cougars in the 1994 WHL Bantam Draft. After being drafted, he played one final season with the Jardine Blazers, recording 38 points in only forty games. The following year, Brewer began his WHL career with the Cougars, playing 63 games in the 1995–96 season. Brewer finished his rookie WHL season with fourteen points, including four goals, and was named Cougars' Rookie of the Year.

Throughout his career, Brewer has represented Canada at various international ice hockey tournaments. He first competed internationally as a member of Team Pacific Canada at the 1995 World U-17 Hockey Challenge in Moncton, New Brunswick. Three years later, he represented Canada as a whole as a member of the national junior team at the 1998 World Junior Ice Hockey Championships, where he was named an alternate captain. This was the tournament in which Canada had its worst ever showing, an eighth-place finish including a loss to Kazakhstan, giving Brewer an unkind welcome to IIHF international ice hockey. Although eligible for the 1999 edition of the same tournament, Brewer was unable to play due to NHL commitments with the New York Islanders.

In his sophomore season, Brewer became a leader on the Cougars' blue line. He was named to play for Team Orr in the 1997 CHL Top Prospects Game in February 1997 at Maple Leaf Gardens. He doubled his point total from the previous season, finishing with 29 points in 71 games played. Brewer followed his regular season by helping the Cougars go on a playoff run. After clinching the last spot in the West Division with a losing record, the Cougars defeated the number-one seed Portland Winter Hawks in the conference quarterfinals and the third-ranked Spokane Chiefs in the conference semifinals before finally losing to the second-ranked Seattle Thunderbirds in the Western Conference final. Brewer finished this run with six points in the Cougars' fifteen games.

Just over a year after being drafted, Brewer signed his first professional contract with his draft team, the New York Islanders, in August 1998. Entering the NHL, Brewer was regarded as a Future Norris Trophy candidate, and as a result, his contract was an entry level three-year, $2.775-million deal complemented by a $1-million signing bonus, the highest base salary available for a rookie. Brewer made his NHL debut on October 10, 1998, against the Pittsburgh Penguins, and on November 5, Brewer scored his first career goal against the Carolina Hurricanes' Trevor Kidd. Throughout his rookie season, Brewer was considered an integral part of the Islanders' defence, and, along with Zdeno Chára, Kenny Jönsson and Roberto Luongo, was considered untouchable by management at the 1999 NHL trade deadline. Brewer finished his rookie season with eleven points in 63 games.

After playing just three games of the 1999–2000 NHL season, Brewer was assigned to the Islanders' AHL affiliate, the Lowell Lock Monsters. It was speculated that the reason behind this move was laziness by Brewer, who was benched during the final thirty minutes by head coach Butch Goring after losing a race for the puck against Mike Knuble in the Islanders' October 11, 1999, loss to the New York Rangers. Brewer also took a bad penalty earlier in the game, putting the Islanders down two men. After a two-week, five-game stint with the Lock Monsters, Brewer was subsequently recalled by the Islanders. After playing 26 games with the Islanders in which he only recorded two assists, Brewer was reassigned to the Lock Monsters on January 8, 2000, for the remainder of the season. Shortly after joining the Lock Monsters, Brewer suffered a sprained knee and missed the next two-and-a-half months of the season. Brewer went on to play 25 games for the Lock Monsters, recording two goals and two assists. He also participated in his first professional playoffs, as the Lock Monsters swept the Saint John Flames in three games in the first round, before being swept themselves in four games in the Eastern Conference semifinals by the Providence Bruins.

At the 2000 NHL Entry Draft, the Islanders traded Brewer, Josh Green and their second round selection (Brad Winchester) in the same draft to the Edmonton Oilers for Roman Hamrlík. Although surprised to be traded, Brewer was excited at the prospect of playing for the Oilers, who saw Brewer as a top-four defenceman. However, Brewer's Oiler career began on a sour note as he suffered a bruised left hip and tailbone in his first game with the team. Brewer missed the next four games before returning to the lineup. Brewer scored his first goal as an Oiler on November 7, 2000, against the New York Rangers. Brewer finished his first Oiler season with career highs in goals, assists and points, as well as the best plus/minus rating on the Oilers team, a plus-15. Further, Brewer gained his first NHL playoff experience, a quarterfinal series versus the Dallas Stars. Brewer had six points, but the Oilers were eliminated four games to two by the Stars.

Brewer made his debut with the Canadian national men's team on April 24, 2001, when he joined Canada for the 2001 Men's World Ice Hockey Championships in Nuremberg, Cologne, and Hanover, Germany. Later that year, on July 24, 2001, Brewer was invited to the orientation camp for the Canadian team for the 2002 Winter Olympics in Salt Lake City, Utah. Five months later, on December 12, 2001, Brewer was named to the final Canadian roster for the tournament. In the opening game of the tournament against Sweden, Brewer scored Canada's second goal of the game in a 5–2 loss, while in the semi-finals of the tournament, Brewer scored the game-winning goal against Belarus in a 7–1 victory, helping send Canada to the gold medal game against the host United States. Canada would go on to defeat the Americans by a score of 5–2, winning their first Olympic gold medal in fifty years.

After a long holdout that lasted until the beginning of Oilers training camp, Brewer finally signed a two-year, $4-million contract in September 2002. At the half of the 2002–03 NHL season, Brewer was named to play in his first NHL All-Star Game, dressing for the Western Conference in the fifty-third edition of the game. He finished with career highs for assists and points and set a career high for goals for the third consecutive season. He appeared in his second NHL playoffs, another quarterfinal series against the Dallas Stars in which the Oilers were once again eliminated four games to two. Brewer finished the playoffs with four points in the Oilers' six games.

Shortly after his Olympic experience, Brewer was named to the Canadian roster for the 2002 Men's World Ice Hockey Championships in Gothenburg, Karlstad and Jönköping, Sweden, his second consecutive Ice Hockey World Championships. He represented Canada once again the following year, when on April 22, 2003, Brewer was named to the Canadian roster for the 2003 Men's World Ice Hockey Championships. In the tournament quarterfinals versus Germany, Brewer scored the game-winning goal 37 seconds into overtime to give Canada a 3–2 victory. Canada would go on to win their first Ice Hockey World Championships gold medal since the 1997 tournament, defeating Sweden 3–2 in overtime in the final. Brewer once again participated for Canada at the 2004 Men's World Ice Hockey Championships, his fourth consecutive Ice Hockey World Championships, where he helped Canada win its second consecutive championship after defeating Sweden 5–3 in the gold medal game.

On May 15, 2004, Brewer was named to the Canadian roster for the 2004 World Cup of Hockey. In the semifinal of the tournament, Brewer scored Canada's first goal of the game in 4–3 overtime victory against the Czech Republic. Team Canada would go on to win the tournament on home ice in Toronto, defeating Finland 3–2 in the final. Just under one year following his World Cup appearance, Brewer was named to the orientation camp for the Canadian team at the 2006 Winter Olympics in Turin, Italy held from August 15–20, 2005, in Vancouver and Kelowna, British Columbia. Following the camp, on October 18, 2005, Brewer was named to the preliminary 81-man Canadian roster for the tournament. However, when the final roster was announced on December 21, 2005, Brewer was not among the 26 players listed. As a result, it would be nearly three years before Brewer would next suit up for his country, when on April 3, 2007, Brewer was among the first five players named to play for Canada at the 2007 IIHF World Championship in Moscow and Mytishchi, Russia. For the tournament, Brewer was named as the team's only permanent alternate captain and helped the team to its third gold medal at the tournament in the past five years.

In August 2005, following the lockout, the Oilers traded Brewer, Jeff Woywitka and Doug Lynch to the St. Louis Blues in exchange for defenceman Chris Pronger. At the time of the trade, Brewer was a restricted free agent, so on August 15, 2005, Brewer accepted the Blues' qualifying offer, signing a one-year, $2-million contract. Brewer's first season with the Blues was a particularly poor one. After playing the first 18 games of the season, Brewer separated his shoulder on November 16, 2005, in a 2–0 victory over the Columbus Blue Jackets. Brewer missed ten games before being activated from the injured reserve list, returning to the St. Louis line-up for a game on December 20, 2005, against the Phoenix Coyotes. Less than a month later, in a game on January 13, 2006, against the Atlanta Thrashers, Brewer collided with the Thrashers' centre Karl Stewart, and dislocated his left shoulder, which ended his season. In just 32 games, Brewer finished his season with nine points, including six goals, two shy of his career best of eight set in the 2002–04 season. Despite his limited play, the Blues re-signed Brewer to a one-year, $2.014 million contract for the 2006–07 season.

Brewer's second season with the Blues began as a disappointment. By the first half of December 2006, Brewer had only amassed six points and a plus-minus rating of –11, often referred to as "the worst player on the ice" by both the media and Blues fans alike. Brewer was often involved in trade rumours, as he was set to become an unrestricted free agent following the completion of the season. Brewer believed his performance was the result of having only played in 32 NHL games since the 2003–04 season. However, after the firing of head coach Mike Kitchen on December 11, 2006, Brewer began playing much better under new head coach, Andy Murray. Over the next nineteen games, Brewer changed his –11 into a +2 and became an integral part of the Blues' defence. His turnaround was rewarded on February 24, 2007, when, rather than being traded as was previously rumoured, Brewer signed a four-year, $17-million contract extension with the Blues. Brewer continued his turnaround through the end of the season, finishing the year with six goals and 23 assists for 29 points, tying his career high for points set in the 2002–03 season and setting a new career high for assists.

In his third season with the Blues, Brewer continued to do well under Andy Murray. Brewer evolved into one of the top two-way defencemen in the NHL, with comparisons being made between him and former first overall draft pick Chris Phillips of the Ottawa Senators. His play and leadership abilities were recognized, when on February 8, 2008, Brewer was named as the nineteenth captain in the history of the St. Louis Blues, filling the vacancy created when former Blues captain Dallas Drake had his contract bought out following the 2006–07 season. On February 17, 2008, in a game against the Columbus Blue Jackets, Brewer set a career high for points in a game with four, all assists, eclipsing his previous career high of three points set on January 16, 2007. Brewer finished the season with only one goal in his 77 games played, his lowest goal total since the 1999–2000 season, although he added 21 assists, three short of a career high. At the completion of the season, Brewer underwent reconstructive surgery on his right shoulder to repair damage suffered in a fight in the Blues' season opening game against the Phoenix Coyotes on October 4, 2007.

On February 18, 2011, Brewer was traded to the Tampa Bay Lightning for Brock Beukeboom and Tampa Bay's third-round selection in the 2011 NHL Entry Draft. In 22 games with Tampa Bay, he notched a goal and an assist. He also led the Lightning in average ice time per game, with 21:34. At the end of the 2010–11 season, Brewer recorded a career-high nine goals and also amassed 81 penalty minutes, good for the second-highest total of his NHL career. He also appeared in a career-high 18 post-season contests with the Lightning in the 2011 playoffs, registering three goals and 17 points, helping the Bolts in their first playoff appearance in four seasons. During the 2011 playoffs, he set a career-high with three points in Game 2 of the Eastern Conference Quarter-finals against the Pittsburgh Penguins and ranked third among all post-season skaters with 51 blocked shots. On June 24, 2011, Brewer signed a four-year, $15.4 million contract extension with the Lightning.

On November 28, 2014, while in the final year of his contract with the Lightning, Brewer was traded to the Anaheim Ducks in exchange for a third-round pick in the 2015 NHL Entry Draft. At the time, Brewer had appeared in 17 games with the Lightning during the 2014–15 NHL season and had four assists on the year. He finished his career with the Lightning having played in 246 games and scored ten goals and 46 assists. The next night, Brewer played in his first game with the Ducks, recording 15:07 in ice time in a 6–4 loss to the San Jose Sharks. On December 3, 2014, after playing in only two games for the Ducks, the team announced that Brewer was expected to miss four-to-six weeks after breaking a bone in his foot from a blocked shot. Brewer returned to the Ducks lineup two months later on February 3, 2015 against the Carolina Hurricanes and scored his first goal for Anaheim on February 8, 2015 against his former teammates in a 5–3 loss to the Tampa Bay Lightning.

Ahead of the 2015–16 NHL season, Brewer was not re-signed by the Maple Leafs and became an unrestricted free agent on July 1, 2015. He spent the summer training in hopes of signing an NHL contract, but realized by mid-August that he was unlikely to find a team interested in his services, and chose not to extend his career by playing in Europe.