Oh man... There are so many in the U.S. But if we limit it to regional accents rather than like Japanese accent to American English and things of the like which makes up for a vast part of "the cultural melting pot" I think there are about 13 regional accents.Appalachian English, Baltimorese, Boontling, Boston English, Cajun English, California English, Coastal Southeastern (Charleston, South Carolina and Savannah, Georgia area), Harkers Island English (North Carolina), Hawaiian English (Hawaiian Pidgin), Hudson Valley English (Albany, New York-area), Inland North American (Chicago, northern Indiana, lower peninsula of Michigan, upstate New York, northern Ohio, part of eastern Wisconsin), Maine-New Hampshire English, New York-New Jersey English, North Central American English (some of Iowa, some of Michigan, Minnesota, North Dakota and some of South Dakota, some of Wisconsin), North Midlands English (thin swath from Nebraska to Ohio), Northeast Pennsylvania English (Scranton, Pennsylvania-area), Nuyorican English, Pacific Northwest English, Philadelphia-area English, Pittsburgh English, Providence-area English, South Midlands English (thin swath from Oklahoma to Pennsylvania), Southern Highland English, St. Louis-area English, Tampanian English, Texan, Tidewater accent, Utah English, Vermont English, Virginia Piedmont, Virginia Tidewater, Wisconsin-Illinois dialect, Yat (New Orleans), Yooper dialect (the variety of North Central American English spoken in the Upper Peninsula of Michigan and in some neighboring areas)
Appalachian English
Baltimorese
Boontling
Boston English
Cajun English
California English
Coastal Southeastern (Charleston, South Carolina and Savannah, Georgia area)
Harkers Island English (North Carolina)
Hawaiian English (Hawaiian Pidgin)
Hudson Valley English (Albany, New York-area)
Inland North American (Chicago, northern Indiana, lower peninsula of Michigan, upstate New York, northern Ohio, part of eastern Wisconsin)
Maine-New Hampshire English
New York-New Jersey English
North Central American English (some of Iowa, some of Michigan, Minnesota, North Dakota and some of South Dakota, some of Wisconsin)
North Midlands English (thin swath from Nebraska to Ohio)
Northeast Pennsylvania English (Scranton, Pennsylvania-area)
Nuyorican English
Pacific Northwest English
Philadelphia-area English
Pittsburgh English
Providence-area English
South Midlands English (thin swath from Oklahoma to Pennsylvania)
Southern Highland English
St. Louis-area English
Tampanian English
Texan
Tidewater accent
Utah English
Vermont English
Virginia Piedmont
Virginia Tidewater
Wisconsin-Illinois dialect
Yat (New Orleans)
Yooper dialect (the variety of North Central American English spoken in the Upper Peninsula of Michigan and in some neighboring areas)
Those are the ones I can think of. I might not have encountered them all though.