The idea of the exemption is based on two Supreme Court cases, 1922's Federal Baseball Club v. National League (which held that in baseball, interstate commerce "was not the essential thing") and 1958's Toolson v. New York Yankees, Inc. (which held that "Congress had no intention of including the business of baseball within the scope of the federal antitrust laws"). But the antitrust exemption doesn't make baseball exempt from labor laws, thanks to Flood v. Kuhn, 1972.
Today there are basically two things that Major League Baseball (an umbrella organization of 30 privately-held companies) can do that most other interstate businesses cannot:
1) MLB can control franchise sales and moves, something no other organization - not even the NFL, NBA, NHL, etc. - can do.
2) The Sport Broadcasting Act of 1961 gives teams in ALL the pro leagues (though not the NCAA) the ability to pool resources to get exclusive TV broadcasting rights. This had previously been ruled illegal under antitrust laws.
As far as MLB is concerned, these are both a big deal. Without #1, baseball teams would be all over the place; for example the SF Giants would have moved to St. Petersburg in 1992. (Which probably means no Devil Rays*). Also, the whole possibility of contracting teams arises from this exemption.
Exemption #2 is probably even bigger - without it, broadcasts could only be made by individual teams, and national broadcasts basically would never happen (unless paid for by very rich teams). This was actually just in the news: Sen. Arlen Specter's threat to revisit NFL's antitrust exemption is why those of us who don't get the NFL Network got to see the Patriots play the Giants last Saturday.
* and if that's not an argument for getting rid of the exemption, I don't know what is!