Craig Kilborn was remembered after Jon Stewart stepped down. Jon Stewart, the longtime host of Comedy Central's The Daily Show, will be leaving this year, according to reports. (AP Photo/Rob Bennett, Mayor's Press Office) Jon Stewart, the longtime host of Comedy Central’s The Daily Show, will be leaving this year, according to reports. And for some reason, this prompted people on Twitter to remember Craig Kilborn, the former host of the Daily Show before Stewart took over.