Shakespeare writes a play set in Cyprus: no magic. Shakespeare writes a play set in Messina: no magic. Shakespeare writes a play set on a Mediterranean island: magic. (?)
At the time that The Tempest was written, the air was thick with tales of the new lands of America, Ireland, and Africa, "brave new worlds" where people did fascinating things like worshiping heathen gods and eating each other. Really, the spectacle of the thing got out of hand. It's no wonder that Shakespeare wanted part of the action. Couldn't help himself.
Shakespeare's Tempest, though it has a comic ending, is generally classified as a "Romance" instead of a "Comedy." Why? Basically, because it has magic in it and it takes place on an island; as for the word "Romance," scholars suspect that the term "Magic Island Story" just wasn't misleading enough.
There are several aspects of Prospero's magical island that seem to draw on contemporary tales of foreign lands. For example, though it was published much later, the Interesting Narrative of the Life of Olaudah Equiano paints a vivid picture of the civilizations encountered by slave traders in Africa; they would have brought back stories of sacrificial worship (which, rather than being associated with classical Jewish worship as Equiano suggests, would quickly gain its own connotations as a barbaric practice), un-Christian systems of morality, unfamiliar superstitions, and strange languages. Enter Caliban, a dark-skinned savage who speaks in flawless iambic tetrameter only as a second language; who feels no shame for having attempted to reproduce with a beautiful woman; who resents being enslaved and tortured; and who wishes such awful misfortune as "wind" and "blisters" upon his masters. He would have been a familiar concept to the common people of Britain, had they been listening to the stories of Africa and America.
Another trope the winds of worldwide conquest would have blown into Great Britain is the shipwreck. "News of shipwrecks reached London regularly during the life of William Shakespeare," writes Hobson Woodward, of the Massachusetts Historical Society. In particular, the story of the Sea Venture, which wrecked in Bermuda, bears particular resemblance to the wreck orchestrated by Prospero and Ariel: they have in common a storm, fierce waves, the terrifying glory of St. Elmo's Fire, and the miraculous salvation of all on board through the presence of an uncharted island nearby (Woodward). Act I of The Tempest contains the pattern every adventurer was familiar with: the peril of the high seas, the unfamiliarity of new lands, and the shocking barbarism of the natives.
Perhaps all this does justify the creation of a new genre for works like The Tempest. In any case, its roots aren't hard to trace in the conquests of British adventurers in strange lands.
Equiano, Olaudah. The Interesting Narrative of the Life of Olaudah Equiano Or, Gustavus Vassa, the African. Ed. Shelly Eversley. New York: Modern Library, 2004. Print.
Woodward, Hobson. "A Jamestown Shipwreck 400 Years Ago This Month Awakened Shakespeare's Muse." History News Network. History News Network, 14 July 2009. Web. 08 Sept. 2015.