With his brother-in-law, Burton Baskin, Irvine Robbins created what has become the largest and best-known chain of ice-cream stores in the world, and some of the jolliest, tastiest and most imaginatively ridiculous ice-cream flavours. In his teens Robbins had worked in the shop connected to his father’s dairy, and boosted sales of ice-cream cones considerably by replacing a sign saying “three scoops of ice-cream, a slice of banana, two kinds of toppings” with the label “Super banana treat”. His playful marketing was central to the success of his own business.

Not only did Baskin-Robbins offer 31 flavours (one for each day of the month), including Rocky Road, Huckleberry Finn, Pineapple Coconut, Very Berry Strawberry, Jamoca Almond Fudge (Robbins’s favourite), Pralines ’n Cream and Chocolate Chip; it also rose triumphantly to special occasions, creating, for example, Astronaut and Lunar Cheesecake in celebration of the successful Nasa space missions of the 1960s; and Cocoa a Go-Go in answer to a craze for go-go dancing.

So much a part of American culture did the company become that one day in 1964 a reporter phoned Robbins to ask what flavour he would be releasing to mark the arrival of the Beatles for an appearance on Ed Sullivan’s TV show. Robbins had nothing planned, but he said “Beatle Nut, of course” — which was being sold in his stores five days later.

Irvine Robbins (known as “Irv”), was born in Winnipeg, Manitoba, in 1917, to a Polish father and Russian mother. The family moved to Tacoma, Washington, where his father became a partner in the dairy. It was when working in the shop that Robbins developed a passion for high-quality ice-cream and realised that the best way to sell it was in a shop that sold “nothing but ice-cream, and could do it in an outstanding way”.

After finishing school Robbins studied at the University of Washington and, when his studies were interrupted by the war, served as a staff sergeant in the US Army, stationed in California. After the war he used a gift of $6,000 from his father to start his own business — Snowbird Ice Cream — in Glendale, California. The opening was delayed because the paint had not dried, and Robbins’s cousin Sybil accounted for most of the first day’s sales, which came to $53, but the shop’s quirky style and inviting atmosphere soon proved popular.

A year later his brother-in-law opened his own ice-cream company, Burton’s, in Pasadena near by. By 1938 the pair had six stores between them, and a decade later 40. In 1949 they bought their own dairy so that they could exercise complete control over how the ice-cream was made. Robbins firmly believed in striving for the highest quality, whatever the cost. The two companies united to form Baskin-Robbins in 1953, and, at the advice of an advertising agency, added “31” to its logo, and started to use pink (cherry) and brown (chocolate) polka dots (reminiscent of clowns and carnivals) in their store decorations and packaging, and cartoons to represent the flavours. They decided to sell stores to managers, a pioneering model for an ice-cream business.

Employees were allowed to eat as much ice-cream as they wanted (Robbins said in 1976 that he ate four scoops a day himself), and customers could taste different flavours free of charge, using the stores’ pink plastic spoons. “Everybody has a proprietary interest in ice-cream,” Robbins once told a reporter. “All you have to do is mention ice-cream and everybody has a flavour.” For him, too, the pursuit of new flavours was constant and feverish. For every eight or nine flavours that arrived in the stores each year hundreds were left in the factory — among them Grape Britain and Ketchup. Customers pitched their own ideas too, occasionally stopping Robbins in his car on seeing his “31 BR” licence plate. (Robbins’s joy in his product also inspired a swimming pool in the shape of an ice-cream cone and a boat named The 32nd Flavor.)

A box of pralines Robbins was enjoying one day with his wife inspired Pralines ’n Cream (which was so popular that it began to sell out, prompting an appeal by the author of the popular syndicated advice column “Dear Abby” — and a petition signed by hundreds of people — for stocks to be replenished). When “Steverino” flavour was invented as a joke on the comedian and musician Steve Allen’s show it was actually made, using fresh fruits and nuts, and sold a million scoops in its first month; and when somebody said to Baskin “Whoever thinks of all these flavors must be plumb nuts!” he replied: “Congratulations. You just invented a new flavour.”

By the mid-1960s there were 400 stores throughout the US. In 1967 Baskin died, and Baskin-Robbins was sold to United Fruit Co for an estimated $12 million, but Robbins continued to work for the company until his retirement in 1978, by which time there were more than 1,600 stores in the US, Canada, Japan and Belgium. Robbins noticed a change in the ice-cream buying American public. “They’re not embarrassed to ask for some of these wild flavours. I think we’ve had a little bit to do with making it more acceptable.”

Baskin-Robbins is now part of Dunkin’ Brands Inc, with more than 5,800 franchises all over the world.

Robbins is survived by his wife, Irma, and by two daughters and a son.

Irvine Robbins, co-founder of the Baskin-Robbins ice-cream parlour chain, was born on December 6, 1917. He died on May 5, 2008, aged 90