That John Frum business was one of the earliest, most widely-reported examples, but most scholars agree that the first documented cargo cult began in 1919, before dying out soon after in 1922. The Vailala Madness, as it was called, gripped people who lived on the Gulf of Papua, a region on the south coast of New Guinea. Rather than getting into the idea of divine beings in the form of some US army guy, however, the Vailala Madness involved people speaking in tongues, fainting a lot and generally acting strange as a result of worshipping an oncoming ghost steamer which they figured might deliver the spirits of their dead relatives to them. Not only that, but the imaginary supernatural ship was alleged to also tinned food, tools, and guns to chase out white colonisers (although the latter point may have been added by worried plantation owners at the time). The religion spread far and wide thanks to the Great British Empire kidnapping and using the local population as slaves elsewhere.
Tom Baker is the Comics Editor at WhatCulture! He's heard all the Doctor Who jokes, but not many about Randall and Hopkirk. He also blogs at http://communibearsilostate.wordpress.com/