H. L. Mencken called rubberneck "one of the best words ever coined." It is easy to see why: the picture of a neck stretching like rubber does all the work.
The word is American and dates from the 1890s. Merriam-Webster dates the verb to 1892 and the noun to 1894. The OED's earliest quotation, cited on the blog Language Hat, is from an 1894 Ohio newspaper. Etymonline gives later dates, 1896 for the verb and 1897 for the noun.
Etymonline's definition of the early noun is a person who is always listening to other people's conversations, or who gazes around with undue curiosity. In the era of shared telephone party lines, a rubberneck was also someone who listened in on other households' calls.
Tourists were an early target. By 1909 the word named the wagons, cars and buses that carried sightseers around cities. Hawkers sold these tours under the nicknames "gape wagons" and "yap wagons." In 1917 the artist John Sloan drew out-of-town visitors as geese in his etching Seeing New York.
The motor car gave the word its modern job. Etymonline notes that it became popular for sightseers in automobiles. Today it most often means drivers who slow down to stare at an accident. The jam they leave behind has names of its own, such as "gapers' delay." In Chicago, the linguist Allan Metcalf noted in 1996, it is a "gapers' block."
That jam is real enough to measure. A study of England's M6 motorway, reported by The Observer in 2009, found that 29% of accidents and breakdowns slowed traffic in the opposite lanes. In 2009 England's highway authority bought 105 sets of incident screens, partitions that hide a crash from drivers on the other side of the road.
The agent noun rubbernecker is recorded from 1934.