A lot of versions of Dragnet have been made, including the original radio show, the original tv show, the reboot with Webb and Morgan, the movie with Hanks and Akroyd, and the tv reboot with Ed O'Neil, but everybody knows you're talking about the Webb/Morgan version when you say Dragnet.
Amazing how much less money was spent on production in those days. Webb and Morgan wore the same suits in every episode, except Webb wore a red sweater in one, where he was taking a college class. They used to splice all the transition scenes across multiple seasons, like them walking to the car, getting out of the car, leaving their desks, etc. Wearing the same suits in every episode let them splice all those scenes in seamlessly.
Both wore dark ties, Webb the gray jacket and black pants, and Morgan the gray suit.
I remember an interview with Morgan when they shut down MASH. He said he told them not to shut the show down, cause everyone was pitching all these projects to them, and that a lot of people didn't realize the show was the star. He said he'd been fortunate enough to be in three legitimate hits (December Bride, Dragnet and MASH,) and while the series were running, everyone wanted him to star in something, and the day the show ended, nobody wanted to know him. According to him, after both December Bride and Dragnet, there were times he became convinced he'd never work again.
Weird thing about some shows is that they become iconic, and you can't really put a finger on why, except they were memorable. Gilligan's Island, the Munsters, Dragnet, the first five seasons of Andy Griffith, Dick Van Dyke, the Beverly Hillbillies and Bewitched are memorable. Some of them were good, some awful, but all are memorable.