I must have seen his show at a friend's house, because I don't remember my parents ever watching Late Night with David Letterman. It was around 1986/87 when I started regularly watching Letterman. I say regularly, but at first that was probably only during the summer, as I had to get up at a ridiculous time to go to school. At some point my Letterman viewing became an every night occurrence, as did after-school naps. The genius of the show was its irreverence, whether it involved Chris Elliot coming out as Marlon Brando or having Teri Garr take a shower. Guests were not worshiped, as Shirley MacLaine and Cher could attest. When Letterman moved to 10:30 at CBS, things were different. The show was watered down, and Letterman was not his cantankerous self. I had better things to do while in college anyway, so that was one more hour in which to do those things. Meanwhile, Leno had taken over The Tonight Show. Leno's monologue was strong, probably a result of Leno's mastery of standup comedy. Letterman, on the other hand, only did two or three throwaway jokes in his Late Night monologue. It was pretty clear that Letterman did not like standup comedy, even though he had done it for a few years back in the 1970s. Nevertheless, Letterman started doing a Tonight Showesque monologue as soon as he took over The Late Show. The differences in the monologues I think was the main reason that Leno eventually commanded a larger audience. Meanwhile, people looked past Leno's horrible interviewing skills and his inability to come up with original comedy bits.
Conan O'Brien was awful when he first started at Late Night. But then he developed a rapport with Andy, and the strong writing overcame the other deficiencies. I thought Conan was in trouble when Andy left, but he held on well enough to command a shot at The Tonight Show. To be cont.