The eminent Shakespearean scholar John Barton has suggested that Shakespeare's accent would have sounded to modern ears like a cross between a contemporary Irish, Yorkshire and West Country accent.
Others say that the speech of Elizabethans was much quicker than it is in modern day Shakespeare productions.
Well, now you can judge for yourself.
Click on the link for sound clips.
Many linguists point to Ocracoke Island, part of the Outer Banks of North Carolina, as being closest to the English of the time of the first English colonial settlements--an English that is often presumed by the same linguists to have changed little in accent at that time since Shakespeare's era.
Somewhat similarly, American spelling in many regards preserves British spelling of the early 1800s, thanks to Webster, more than current British spelling does. Melvyn Lord Bragg highlights this fact--with examples--in his 2003 documentary, The Adventure of English.