(FORTUNE Small Business) – At a Cincinnati dinner party in 1845, John Brunswick, a Swiss immigrant carriage maker, saw his first billiard table, a British model with dazzlingly ornate details. Brunswick knew little about billiards but plenty about woodworking, and he was transfixed by what he saw. Within months his carriage shop turned out its first billiard table, and soon he had abandoned carriages altogether to concentrate on billiards--not just tables but also balls and cues. Brunswick's timing was perfect: He moved into billiards just as the game became popular in America, and his superior craftsmanship cornered the market. By 1885, shortly before his death, Brunswick's business was the world's biggest billiard-equipment operation.

The unlikely shift from carriages to billiards was the first in an extraordinarily wide-ranging series of moves that would make Brunswick's operation one of the most diversified companies in the world. Perhaps most impressive, those moves displayed an intuitive knack for synergy that would put modern corporations to shame.

Moses Bensinger, Brunswick's son-in-law and successor, saw expansion opportunities beyond billiards. Noting that his tables were appearing in more taverns and saloons, Bensinger focused the company's woodworking acumen on beautifully carved bar fixtures, which became big sellers in the 1890s. And since many of those drinking establishments were also installing bowling lanes, Brunswick moved into that industry too, manufacturing balls, pins, and lane surfaces. In 1895, Bensinger himself helped form the American Bowling Congress, which standardized the game's hodgepodge of rules and is still its governing body today.

Bensinger's son Benjamin elevated the company's synergistic efforts to an art. Anticipating the coming of Prohibition, he took Brunswick out of the bar-fixture business in 1912. (Prematurely, as it turned out: The 18th Amendment didn't pass until 1919.) With the firm's skilled woodworkers needing new projects, Benjamin set them to making spectacularly ornate phonograph cabinets. But Benjamin was irked that the cabinets were merely the housing for the phonographs themselves--why couldn't Brunswick manufacture those too? By 1916 it did. Employing a similar logic, he saw no reason why a Brunswick turntable couldn't be playing Brunswick recordings, so in 1922 he started the Brunswick record label. Over the years its roster of stars included Duke Ellington, Benny Goodman, and Jackie Wilson. In one generation, Benjamin transformed Brunswick from a leisure brand into an entertainment dynamo.

Brunswick's steady growth generated several important innovations, including the world's first hard-rubber bowling ball (1906) and the first automatic pinsetter (1956), which revolutionized the bowling industry, and the first rubber toilet seat (1912), which revolutionized ... well, you get the idea. The company had a golden touch, from its bestselling Blue Flash tabletop refrigerator (1933) to school furniture (1952), most notably the stackable molded-plastic chairs that were ubiquitous in my high school cafeteria and probably yours too.

The family gave up voting control in 1966, but Brunswick's tradition of leisure-time diversity continues. In addition to remaining a top bowling and billiards brand, Brunswick is a major player in the fitness-equipment market and is also the global leader in marine engines and pleasure boats--a pairing that would no doubt have pleased Benjamin Bensinger. Of course, he'd probably have pushed to have Brunswick open its own chain of marinas too.