Before becoming a professional baseball player, he majored in sociology at the University of California, Berkeley and played for the California Golden Bears baseball team. In 1993, he played collegiate summer baseball with the Brewster Whitecaps of the Cape Cod Baseball League.

On March 12, 2002, after playing in Montreal for three years, he was traded to the Houston Astros in exchange for Chris Truby.

He was then traded after the 2003 season to Tampa Bay Devil Rays in exchange for Brandon Backe. In 2004, he batted only .215 for the Devil Rays, with a .266 OBP.

Blum signed with the San Diego Padres as a free agent on December 9, 2004. He hit .241 in 78 games for the Padres in 2005.

He was traded to the Chicago White Sox for a minor leaguer on July 31, 2005.

On October 25, 2005, Blum hit a home run against the Astros at Minute Maid Park in the top of the 14th inning to win Game 3 of the World Series.

On November 20, 2007, Blum signed a $1.1 million, one-year contract with the Houston Astros. The deal also included a club option for 2009.

On April 11, 2008 a monument celebrating the 2005 World Series was unveiled at U.S. Cellular Field in Chicago, featuring bronze statues of five players. Blum is one of them, commemorating his tie-breaking home run. The home run would forever cement his place in White Sox history.

Blum returned to the Astros in 2009 and played mostly 3B for Houston. He hit 10 home runs that season, drove in 49 runs and was known for playing excellent defense at all the infield positions.

On October 30, 2009, Blum re-signed with the Astros. The contract was worth $1.5 million for the 2010 season and included a mutual option for 2011, which would be worth $1.65 million that was declined, making him a free agent.

Blum suffered a season-ending injury to his elbow in July 2010 while putting on his shirt after a game. He had this to say: “There are probably 90 percent of us in the big leagues that have loose bodies floating around. It just so happens that after the game, it tightened up on me. The shirt had nothing to do with the damn injury.”

On November 15, 2010, Blum signed a two-year contract worth $2.7 million with the Arizona Diamondbacks. In 2 years with the Diamondbacks, he appeared in a total of 40 games out of 326 possible games due to injury. He was released by the Diamondbacks on July 20, 2012.

On January 12, 2013, he was named a color analyst of the Houston Astros. He is teamed with Todd Kalas, who is handling play-by-play. At the end of the 2019 Season, the Astros announced that Blum and Kalas will return as broadcast partners for the 2020 season.