As an American I know of several clearly distinct accents. I coined names for some of them myself since I do not know if they have a real name.
Regular(spoken on the west coast, southern Florida, all the major cities.)- It is spoken by the majority of Americans, on sitcoms and commercials.
Country - Spoken mostly in the south, some places in the midwest and just inland of the west coast.
New York - Spoken mostly in the different burroughs of NYC(Brooklyn, Queens, etc.)
Boston - Spoken in and around Boston.
Upper-class - Spoken among the extremely wealthy class on the east coast. Bears some resemblance to English.
Chicago - Not spoken by all Chicago Natives, but definitely distinct to a trained ear.
Cajun - Spoken in Louisiana. Sounds like a combination of American and French, or an American with a French accent.
Hawaiian(Pidgin) - A slang developed among the Hawaiians, Japanese, Chinese, and Portugese. Very much it’s own language(in the spoken form). It can be unintelligable to the average American.
Native American - An accent spoken by some Native Americans. Again very distinct.
Latino - Prevalent among Mexican Americans. Even though they may not speak much Spanish, they retain an accent like they are Mexican.
Ebonic(for lack of a better word) - Spoken by many of the black population and by Eminem.
Canadian Accents.
I can only think of two that I know.
Western Canadian - Essentially regular American, but wierd pronunciations on many words.
Victorian - Many Residents of Victoria, BC, have retained a British Accent since the British settled in different places in the Puget Sound.
These are all I can think of but I am sure there is more. American’s if you can think of any more.