A wonderful example of this is seen in the first episode of the series in which Maigret is in the middle of a long term investigation involving a series of jewel store robberies that have been plaguing Paris for years. He is convinced he knows who is behind the crimes, but he has been unable to collect the proof he needs to put the man behind bars. You'd think he'd have a slightly antagonistic relationship with his suspect, yet the two men treat each other with the utmost respect and courtesy. When his long time opponent is found shot to death in his apartment, Maigret treats the case like its an investigation into the murder of a friend.
The cases are a diverse mix of circumstances and locations, and while the majority of them revolve around murder, there is also some political intrigue and corruption included which make for a nice change of pace. What's refreshing about the series is no matter what the crime, the writers have ensured we realize how much of a police investigation is drudge work. Clues are discovered from careful examinations of files, researching a person's history and going door to door to try and talk with potential witnesses. Maigret and his team of three detectives work long hours on a case sifting through evidence and piecing together the facts. This doesn't mean there's no action. Far from it in fact as the boring stuff takes place off camera and we only see them acting on the information they've uncovered.
Still, there's very little of the type of action North American audiences are used to in their police shows. The joy in this show is watching Maigret's interaction with the various characters he interviews and comes in contact with over the course of his investigation. Watching Gambon come to a slow boil and struggling not to let it show when Maigret is dealing with a particularly odious political boss or allowing his incredulousness at someone's obvious fabrication to show through the arching of one eyebrow is more fun than any car chase or gun battle you'll ever see.
One of the other treats of this series are some of the other actors who show up in various episodes. Most memorably is the episode where Maigret is investigating the death of a young night club stripper. Not only is the stripper played by Minnie Driver but the same episode features a young morphine addict played by the wonderful Michael Sheen and the stripper's boss is played by Brenda Blethyn. The series originally aired in 1992 and 1993 so it was before any of the three had achieved the level of notoriety they enjoy today, but one can see in each of their performances why they have gone on to be so successful.