The version most familiar is that boxy, 1950s-indebted shape that plied US cities for decades as a taxicab. The formula was simple: salon-size rear passenger area, complete with sofa-like back seat and two small jump seats; a cavernous trunk; and a durable engine from a US automaker, usually General Motors.

The Checker Motors Corporation stopped making cars in 1982 – about the time that Taxi, a sitcom on US television that did much to stoke the Checker’s legend, also concluded. The last time a Checker collected a fare in New York, the city with which it is synonymous, was in 1999.

But the cars maintain a following. Some people keep models in running order for use in films and television. Others simply like them for what they evoke. Still others love the cars for the community that has risen around them in their dotage.

What sort of people join Clan Checker? "Oddballs," said Michael Angelich, of Long Island, New York, at the annual Checker Car Club of America gathering in Brooklyn. Although he no longer owns a Checker, he claims to have owned several over the years, and still serves as the club's historian.

"They're funky cars; the only people who wanted them who weren't cab drivers were people with big families," Angelich said, adding that by the time Checker stopped making the cars, they had already been considered outdated for years, not having changed much since their last major redesign, in 1956. "The taxi fleets liked them because if you smashed a fender, the parts were the same every year, whereas a Chevy or a Ford changed every year."

The collection of cars assembled on the street in Greenpoint, a neighbourhood at the northern reach of Brooklyn, ranged from President Carter-era liveried New York City taxicabs to stretched, multi-row Aerobus station wagons. There were also quite a few Checker Marathons, the limited-run passenger cars built by Checker from about 1960 until the company foundered.

Members had driven from all US points to reach the convention.

Ron Leatz, who travelled from Dowagiac, Michigan, in his rare 1979 Checker Marathon factory demo model, had a sheaf of papers documenting how few "civilian" Marathons were built. According to his records, production peaked at a few hundred per year, and by 1979, when his car was built, only 168 rolled off of the Checker assembly line in Kalamazoo, Michigan.

"When you see Marathons, they're survivors of the civilian side of the business," he said, adding that there were now fewer than 800 Checkers of any type left in the world.

Many people assume that Checkers, like cockroaches, will last forever. But according to the club’s website, this is pure myth. The type of steel Checker Motors used was thick, but susceptible to rust. Although rust has eaten some Checkers in their later years, most of them didn't get the opportunity to rust out, having been thrashed beyond the point of salvation in their bruising daily rounds on the US’s busiest streets.

Anne and Jim Chanas, from Elon, North Carolina, were less focused on the history of the company and more versed in the details of their particular car. They bought the 1972 Checker Marathon in 1974 from Anne’s brother, who was shipping off to the Air Force and needed to sell it. The dark red Marathon was put into service as the Chanas’ family car, and eventually benefitted from extensive body repair to fix the many rust holes that had accumulated over the years.

"You see how much room there is in the back?" Chanas said, pointing to the large expanse of floor between the front and rear seats. "We had little kids and they would stay back there with sleeping bags when we travelled. That was back before seat belts and car seats."

Chanas said there were never many Checkers in North Carolina, and recalled getting some strange looks.

"One time I drove to the farmers’ market, and the man put a bushel of beans or whatever inside and said, 'Is this a Rolls-Royce?'"

Paul Worth drove his 1972 Marathon up to Greenpoint from Quitman, Georgia. Although Checker Motors put proven but lacklustre engines under the hood, Worth's car packs more of a punch, thanks to the General Motors Performance Parts crate motor he dropped in. He says it will do 100mph. without a problem. To make it more suitable for long road trips, he installed modern seats, an overdrive transmission, cruise control and aluminium wheels from a 1990s Chevrolet van.

Checkers first came onto Worth’s radar during a visit to Chicago in 1980.

"I was just standing there in front of the Museum of Science and Industry, watching all of the different-coloured Checker cabs go by, and I fell in love," he said. "Years later, I had an opportunity to buy one."

Victor Coiro, from Brooklyn, carries himself like a Taxi cast-member, thick New York accent and all.

"I'm a bit of a Checker nut," he said. Though he had just sold two, he still owned three taxicabs and a station wagon. He said that it has always been difficult – even 25 years ago, when the cars were more common – to find correct front fenders for them. Angelich interrupted the lament.

"I got one I can sell you," he said, demonstrating how these clubs function not only as social organisations, but as a means for its members to keep their cars on the road.

Arthur Jenkins, from Powhatan, Virginia,  has owned two cars in his lifetime, both  1960s Checkers. He still has them.

"I fit right in with these people," he said. "They're really not about the cars. They're outgoing, and gregarious, and the car is just a means of engaging people."

The club's motto, he said, neatly sums up the Checker hobby: "A Checker owner is never alone."

If you would like to comment on this story or anything else you have seen on BBC Autos, head over to our Facebook page or message us on Twitter.