Many criminals made the mistake of underestimating Lieutenant Columbo, a homicide investigator with a crumpled trench-coat and a beat-up car, who certainly acted as an incompetent bumbler.
But he was so polite to every suspect, and he talked so much about his wife (who we never got to see on any episode, but who many believe later had her own show, starring Kate Mulgrew, later of Star Trek: Voyager fame) that he lulled even the shrewdest murderer into a false sense of security.
And although the audience had witnessed the murder in the beginning of each episode, it was still a surprise to see what mistakes the killers had made during the seemingly perfect murder.
Peter Falk carried the old trench-coat for 7 seasons of 90 and 120 minute movies on NBC, before the series ended. But over a decade later, Falk agreed to revive the character on ABC for an additional 2 seasons with a subsequent string of TV-movies with the loveable detective once again using his calling-card false good-byes: "Oh, there´s just one more thing..."
(A note on the running time of the episode: During the first 7 seasons, 18 episodes were 120 minutes long, while the other 27 episodes were 90 minutes long. The episodes after that were all 120 minutes long. In the episode guide, I have only marked out the 90 minute-episodes.)