Conan O'Brien and David Letterman were rivals for all of seven months when Conan hosted The Tonight Show. Clearly that wasn't enough time to create bad blood, as Conan wrote a gushing essay about Letterman for Entertainment Weekly. He recalls watching Letterman's short-lived morning show in high school and Late Night being a staple for him and his friends in college. In Conan's book, Letterman's innovations are as great as the light bulb and Twix Bar. 

Here's an excerpt with Conan describing what made Letterman special:

Dave’s show was that rare phenomenon: a big, fat show business hit that seemingly despised show business. Dave didn’t belong, and he had no interest in belonging. He amused himself, skewered clueless celebrity guests, and did strange, ironic comedic bits that no one had seen on television before. Everything about that show was surreal and off-kilter. Where late night television had once provided comfort, this man reveled in awkwardness. Cher called him an asshole. Andy Kaufman ran screaming from the set. Chris Elliot lived under the stairs. Throughout one episode the entire show rotated a complete 360 degrees, for no reason whatsoever. By 1985, when I graduated from college and was ready to try my hand as a comedy writer, Late Night with David Letterman had been the Holy Grail for several miraculous years.

Make sure you read the entire essay here. However hard Letterman's departure hits you, you won't be as emotional as Conan.