“This American Life” has always been one of my favorite podcasts (my father and I used to go on trips and listen to that on the way). They do a couple things extremely well that keeps me interested.
The stories they choose, while not outrageously “out there” or crazy, are interesting yet still relatable which keeps me coming back and wanting to hear more. For all I know, it could be me or someone I know. These stories are just out there enough that I want to hear more, but they really are relatable. They also take amazing advantage of the story arc, they slowly build up to the climax so I always want more.
The biggest thing they do to keep the continuity of the story going is how they pace themselves and how they fill in the pauses they make. They always have suspenseful music playing or music to fit the mood of the situation that is going on, and the background music is soft enough to pay attention yet still set the mood.