The precursors of rum date back to ancient times, with historical evidence dating back to the Middle Ages. The development of fermented drinks produced specifically from sugarcane juice is believed to have first occurred in either ancient China or India, and is believed to have spread from these regions. An example of an early 'rum' drink is known as 'brum'. Brum is known to have been produced by the Malay people, scientific dating of brum, dates it back thousands of years. Marco Polo noted in the 14th-century of a "very good wine of sugar" that was offered to him in the area that became modern-day Iran.

The first distillation of rum took place on the sugarcane plantations of the Caribbean in the 17th century. The plantation slaves first discovered molasses, a byproduct of the sugar refining process, could be fermented into potent alcohol. Later, distillation of these alcoholic byproducts concentrated the alcohol and removed impurities, producing the first true rums. Tradition suggests rum first originated on the island of Barbados. However, in the decade of the 1620s, rum production was recorded in Brazil. A liquid identified as rum has been found in a tin bottle found on the Swedish warship Vasa, which sank in 1628.

The origin of the word "rum" is generally unclear. In an 1824 essay about the word's origin, Samuel Morewood, a British etymologist, suggested it might be from the British slang term for "the best", as in "having a rum time."

'As spirits, extracted from molasses, could not well be ranked under the name whiskey, brandy, or arrack, it would be called rum, to denote its excellence or superior quality.' - Samuel Morewood

Given the harsh taste of early rum, this is unlikely. Morewood later suggested another possibility: that it was taken from the last syllable of the Latin word for sugar, saccharum, an explanation commonly heard today.

Other etymologists have mentioned the Romani word rum, meaning "strong" or "potent". These words have been linked to the ramboozle and rumfustian, both popular British drinks in the mid-17th century. However, neither was made with rum, but rather eggs, ale, wine, sugar, and various spices. The most probable origin is as a truncated version of rumbullion or rumbustion. Both words surfaced in English about the same time as rum did (Coromines states 1651 as the first recording of "rumbullion", and 1654 for "rum" -1770 for the first recording in Spanish of ron), and were slang terms for "tumult" or "uproar". This is a far more convincing explanation, and brings the image of fractious men fighting in entanglements at island tippling houses, which are early versions of the bar.

The American colonies were rum-crazy. In fact, much of the sugar was shipped to New England to be turned into rum. And major New England rum makers dominated until the mid-19th century and from then forward, the Caribbean and Latin America, where the sugar originated, became the production centers. The American colonies favored rum over whiskey or gin. And the New England distilleries controlled the market until Americans started to prefer bourbon. The American colonialist liked aged dark rums that got much of their taste from the oak barrels that the rum was aged in.

Rum had a particularly strong connection with sailors. Privateers and pirates were notorious rum drinkers. As often ships crossing the Atlantic had barrels of rum, they had no shortage of it. At one time, it was such an important commodity that rum became a currency for a short period. Rum was also the drink of navies. In particular, the British navy gave a certain portion of rum to sailors. This tradition lasted for more than 200 years and only recently ended.