Here's a couple of episodes from The Lawless Years an NBC crime show that aired for three seasons from 1959 - 1961. It starred James Gregory who is best known as Inspector Lugar on Barney Miller. In this series he plays Barney Ruditskya real life NYC detective.
The Nick Joseph Story stars a young Vic Morrow.
Smooth and debonair Peter Gunn was a different kind of private eye. His office was a hip club called Mother's and jazz music provided the background score. Director Blake Edwards went on to a successful film career The Pink Panther being his most notable achievement.
Gang Busters was a true crime multi media franchise; radio show that ran for 21 years , a comic book and film serial. In 1952 it was this short lived TV series that has the distinction of being the highest rated show to be cancelled. It ran alternate weeks with Dragnet another popular radio show making the leap to the small screen. As popular as it was Dragnet was a monster so bye bye Gang Busters.
Man With A Camera
A late 1950's ABC series that starred Charles Bronson as Mike Kovac a WW 2 combat photographer turned photographer / private eye. A bit of a technologist Kovac has a phone in his car, a darkroom in a trunk and an array of hidden cameras. The series lasted for two seasons with a total of 29 episodes.
Raymond Chandler's Phillip Marlowe became a half hour television series that aired on ABC for 26 episodes in 1959/60 "Murder Is A Grave Affair" was #23. A star struck young woman is involved with a famous Hollywood director. She then dies under mysterious circumstances.
More Marlowe " The Ugly Duckling" is the first. Donna Raymond is a vixen who has her claws in David Jordan, a married man. He is a lawyer who looks after his wealthy wife's interests. Donna arranges to have someone run Mrs. Jordan off the road but she survives. At this point Marlowe is called in by Paul Howard who is Mrs. Jordan's father.
Debuting in 1949 Martin Kane has the distinction of being TV's first private eye show. It lasted for five seasons with four different actors (including Loyd Nolan) playing the lead role. It was also the first show with commercials built into the show. Each episode featured a visit to Happy McMann's Tobacco Shop where the virtues of the shows sponser U.S. Tobacco was presented.