What is the correct punctuation after the salutation of a letter--a colon, semicolon, or comma?

Either a colon or a comma may be used, depending upon the degree of formality desired.

A colon follows the salutation in formal letters:

Dear Ms. Gregorson:

Members of the Board:

A comma follows the salutation in informal letters:

Dear John,

Edward,

The use of a semicolon after a salutation is improper.