It is fun to watch Kraft Suspense Theatre just to see what classic cars will appear in the show. KST is not unique among 1960's programs in this regard. Many shows from that era feature (now) classic automobiles. But many shows had limited budgets with few outdoor shots. Many exterior car shots from other shows featured the vehicle either indoors or in an obviously indoor studio made to look like an outdoor street.
The KST car shots took place outdoors - at least the shots of car exteriors. KST usually avoided the cliched car chase, but found numerous ways to use vehicles to contribute to the drama. Even when the cars were not the center of the drama, they made the action seem more realistic. They also added class to the show.
It seems to me that the 1963 Mercury Monterey was used in many episodes. [I may change my mind about that when I start reviewing individual episodes.] The 1963 Monterey was unique because it had a powered, backwards rear window that could be raised and lowered. The window design was called "Breezeway." The 1963 model was unmistakeable, even if most cars of that era look the same to those of us that grew up in the 1970's.
1963 Mercury Monterey "Breezeway"
From the ad, it appears that one reason for this feature was to allow cigarette smoke to escape from the rear of the car. Based on that possibility, it does not appear that we will see many more cars with the Breezeway feature in the future.
update - click the following for discussions of:
the theme music;
connections between Kraft Suspense Theatre and Star Trek;
The RTV network and prior syndication.