The Late Night With Conan O'Brien Wikipedia page explains what started the fight:
Recently, Stephen Colbert made the claim that because of "the Colbert bump", he was responsible for Mike Huckabee’s success in the 2008 presidential race. Conan O’Brien claimed that he was responsible for Colbert's success because he had made mention of him on his show. In response, Jon Stewart, host of The Daily Show, claimed that he was responsible for the success of O‘Brien, and in turn the success of Huckabee. This resulted in a three-part comedic battle between the three pundits, with all three appearing on each other's shows. The feud ended on Late Night with an all-out brawl between the three talk-show hosts.
Additionally, "Late Night Underground", which is a blog run by a person(s?) associated with Late Night With Conan O'Brien, just released a video featuring the outtakes of this fake fight. It's terrific. Sorry I couldn't figure out how to get it on the site, so go to that link. It's 5 minutes, and again, it's well worth your time. Also, that website is awesome for fans of Conan. I'll add a link on the "Sites We Like" list.