The various Germanic tribes (Angles, Saxons, and Jutes) who invaded Britain after 437 AD brought with them slightly different dialects of West Germanic. These formed the basis for the emergence of later dialect areas in the British Isles. The Viking invasions (8th-9th centuries) contributed yet another layer to the existing dialects by affecting the northeast of England more than in the south and west. The Norman French invaders (11th century), conversely influenced the south more than the north, which came to be more conservative linguistically. The Great Vowel Shift of the 1500's didn't affect northern English dialects, which came to be called Scots English. Because of the long history of dialect creation in the English speaking areas of Great Britain, there are more dialects of English in Britain than in America, Canada, and Australia combined. British colonization of other continents led to the establishment of various colonial, or overseas, dialects. These dialects developed because of the following three factors: 1) the dialect of British English spoken by emigrants who first established the colony--the so-called founder's effect; 2) mixing with some non-English language in the colony--the so-called substrate effect; 3) mixing with other dialects in the colony--the leveling effect of dialect mixing. Thus, overseas English dialects came to differ from dialects in Britain, a process additionally enhanced by innovation in British English which did not occur in the more conservative overseas dialect.
The main dialect areas of the US can be traced to four migrations of English-speaking people to what is now the United States from the British Isles during the colonial period (1607-1775).
1. From 1629-1640 Puritan religious dissenters fleeing oppression from Charles I fled East Anglia and brought their distinctive twang to Massachusetts. Their dialect eventually influenced speech in many areas of the Northeast. Except in New York, it was not mixed significantly with any non-English speech. New York English developed when in 1664 the British took possession of the Dutch colony of New Netherlands, setting in motion the gradual conversion of Dutch speakers to English. The Dutch left a substrate which sets Brooklyn speech apart from other dialects. Also, Jewish immigrants from Eastern Europe speaking Yiddish added their own flavor to New York speech.
2. From 1642-1675 the Royalists, also called Cavaliers, fled from the south and southwest England with their indentured servants and settled in Virginia when the English Civil War against Charles I began. They brought their south English drawl with them. Royalists later came to the Carolinas as well. Southern English speech laid the foundation for the development of American Tidewater, or Coastal Southern English, which in turn was influenced--particularly in phonology-- by the speech of Africans brought as slaves. These Africans, in turn, adopted the tidewater drawl and various particulars from the English of their masters. However, mixed in were elements from the phonology of West African languages. Some West African words and grammatical patterns were also retained in what has come to be called Black English. After the Civil War, Black English continued to evolve and change, especially in the creation of new vocabulary. In the coastal area of Georgia and South Carolina, the descendants of Africans preserved much more native African in their speech; an African-English creole called Gullah is still spoken there by about 20,000 people. The Cajun French in Louisiana also adopted English with noticeable traces of their former language.
3. From 1675-1725 the Quakers, members of the Society of Friends, migrated from the north Midlands of England and Wales to the Delaware valley. Their speechways--mixed with earlier Swedish and later German immigrants such as the Amish--gave rise to the distinctive band of dialects spoken in parts of New Jersey, Delaware and Pennsylvania, notably the Philadelphia area.
4. From 1718-1775 English speakers left North Britain and Northern Ireland and settled in the Appalachian backcountry. These people are called the "Scots-Irish." These were mostly Anglo-Saxons refugees of the Norman Conquest who had settled within the Celtic fringe of Britain. The true Scottish and Irish people were Celts who spoke Scots-Gaelic or its close relative Irish-Gaelic and most did not adopt English until the 18th or 19th century. The immigration of true Irish and Scottish peoples, beginning in the mid 1800's, had little permanent effect on American dialect formation; nor did most other 19th and 20th century immigrant groups. (Interestingly, most Americans who claim Scots-Irish ancestry are really Anglo-Saxons with little or no true Scottish or Irish ancestry; and many southern Americans who consider themselves "English" would actually find their ancestors were Norman French.) The "Scots-Irish" dialect of southern English mingled with Cherokee and other Native American languages. It is occupied band running from western North Carolina to Oklahoma and East Texas, giving rise to the so-called backwoods, or highlands, southern dialect, which is faster and higher-pitched than tidewater southern and more nasal than Appalachian English.
5. After the War Between the States the rapid and extensive move West of settlers from all dialect areas of the eastern US led to a leveling of eastern dialectal features and the creation of a more General American, or Middle American dialect. People who are said to speak "without an accent" are actually speaking with this leveled-out western accent. Now, this western, "leveled" English is itself showing signs of dialect genesis. Listen to a teenager from California if you don't believe me. The history of American English and of English is far from over.