Source: PBS: Pioneers of Television- Bob Newhart Listens Funny
Bob Newhart's unique sense of humor was the thematic core of the Bob Newhart Show. If you are wondering who the Bob Newhart Show was named after, you are probably also wondering what state Florida is in. I make that crack because it is a pretty good example of Bob Newhart's sense of humor. It was very dry, like the Mojave Desert, with no real physical or emotional expression. He would say very funny lines with a completely straight face.
Newhart played psychologist Bob Hartley, who lived and ran a private practice in Chicago. He played himself in the role as a very straight-laced, almost totally unemotional person who delivered a lot of great lines as if he were on stage. This is sort of hard to explain in writing but he would deliver great sarcastic lines with a straight face that someone who isn't very quick or lacks a great sense of humor could easily take seriously. Anyone with a quick wit could easily tell that he was joking.
To give you an example, Bill Daily who played the Hartley's neighbor in their apartment building was always coming over without knocking on the door first and would just walk in. After he would come into the Hartley apartment, Dr. Bob would say, "Come in Howard," after Howard was already in the apartment. That might sound simplistic and trivial but Newhart had such a quick and accurate way of uttering such lines that they were hilarious.