THE ROYAL MYSELF

Myself is going shopping.  To me, that sounds horrible.  Sue and myself are going shopping.  Same thing.  It sounds like fingernails scraping on a chalkboard.  Of course, I realize that schools do not teach grammar anymore.  Unfortunately we are now hearing very strange things.  Me and him are going fishing.  That type of speech has been around for a long time and I actually blame cookie monster for it.  Cookie monster uses "Me" as the subject of the sentence all the time, e.g. "Me like cookies."  I really blame Sesame Street for a good deal of bad grammar.  But the use of "myself" is more recent.  Maybe it is like the British cockney in reference to the King of England:   "Himself is about to speak."  It sounds more important or even royal.  Myself is about to speak:

Myself is a reflexive pronoun.  It is used to refer to the subject or to emphasize the subject.  "I did the report all by myself." Or, "I,myself, wrote the report."  I myself repaired the plumbing.  I did it all by myself.
I did the shopping all by myself, but myself did not do the shopping. 

The pronouns I and we are nominative, the subject of the sentence.
                        I went shopping.  We are going fishing.  Joe and I are going fishing.
                        I caught the fish all by myself.  I, myself, caught the fish!

Me and us are objective pronouns. 
                        Give the report to me.  Give the report to us.  Report to us at 8:00A.M.
                         Give the report to myself? NO NO 
                         I wrote the report all by myself.
                         Tom, Dick, Harry, and I wrote the report.  (NOT Tom, Dick, Harry and myself...)

Myself, herself, himself, themselves are reflexive. 
                         They did it all by themselves.
                          She did it all by herself.
                          He did it all by himself.
                          I did it all by myself

Myself wrote this all by myself.