From the Chicago Manual of Style - 16th Edition - 8.46:
Terms that denote regions of the world or of a particular country are often capitalized, as are a few of the adjectives and nouns derived from such terms. The following examples illustrate not only the principles sketched in 8.1 but also variations based on context and usage. For terms not included here or for which no suitable analogy can be made, consult Webster’s or an encyclopedia: if an otherwise generic term is not listed there (either capitalized or, for dictionary entries, with the indication capitalized next to the applicable subentry), opt for lowercase. Note that exceptions based on specific regional, political, or historical contexts are inevitable and that an author’s strong preference should usually be respected. See also 8.45.
the Swiss Alps; the Australian Alps; the Alps; an Alpine village (if in the European or Australian Alps); Alpine skiing; but alpine pastures in the Rockies (see also 8.52)
Antarctica; the Antarctic Circle; the Antarctic Continent
the Arctic; the Arctic Circle; Arctic waters; a mass of Arctic air (but lowercased when used metaphorically, as in “an arctic stare”; see 8.60)
Central America, Central American countries; central Asia; central Illinois; central France; central Europe (but Central Europe when referring to the political division of World War I)
the continental United States; the continent of Europe; but on the Continent (used to denote mainland Europe); Continental cuisine; but continental breakfast
the East, eastern, an easterner (referring to the eastern part of the United States or other country); the Eastern Seaboard (or Atlantic Seaboard), East Coast (referring to the eastern United States); the East, the Far East, Eastern (referring to the Orient and Asian culture); the Middle East (or, formerly more common, the Near East), Middle Eastern (referring to Iran, Iraq, etc.); the Eastern Hemisphere; eastern Europe (but Eastern Europe when referring to the post–World War II division of Europe); east, eastern, eastward, to the east (directions)
the equator; equatorial climate; the Equatorial Current; Equatorial Guinea (formerly Spanish Guinea)
the Great Plains; the northern plains; the plains (but Plains Indians)
the Midwest, midwestern, a midwesterner (as of the United States)
the North, northern, a northerner (of a country); the North, Northern, Northerner (in American Civil War contexts); Northern California; North Africa, North African countries, in northern Africa; North America, North American, the North American continent; the North Atlantic, a northern Atlantic route; the Northern Hemisphere; the Far North; north, northern, northward, to the north (directions)
the Northeast, the Northwest, northwestern, northeastern, a northwesterner, a northeasterner (as of the United States); the Pacific Northwest; the Northwest Passage
the poles; the North Pole; the North Polar ice cap; the South Pole; polar regions (see also Antarctica; the Arctic)
the South, southern, a southerner (of a country); the South, Southern, a Southerner (in American Civil War contexts); the Deep South; Southern California; the South of France (region); Southeast Asia; South Africa, South African (referring to the Republic of South Africa); southern Africa (referring to the southern part of the continent); south, southern, southward, to the south (directions)
the Southeast, the Southwest, southeastern, southwestern, a southeasterner, a southwesterner (as of the United States)
the tropics, tropical; the Tropic of Cancer; the Neotropics, Neotropical (of the New World biogeographical region); the subtropics, subtropical
the Upper Peninsula (of Michigan); the upper reaches of the Thames
the West, western, a westerner (of a country); the West Coast; the West, Western (referring to the culture of the Occident, or Europe and the Western Hemisphere); west, western, westward, to the west (directions)