Save "me", please

English may be a living language, but the proper use of "me" is dying. Often bad language comes up from the bottom: kids, TV shows, wrestling matches. Over the last ten years, an error that bugs me came down from the top, from adults, from professionals. It is the use of the word "myself" when the speaker or writer means "me."
e.g. Turn your documents into Kevin or myself by 3:00.
e.g. (worse) Dave and myself will be away tomorrow. (should be "I")

I turn in documents to you, not to yourself. I see her, she sees herself. You play with me, I play …

On second thought, I guess the word "me" is not imperiled as I first thought. Almost every student says "Me and her are going to the mall." Hearing that always gives myself a headache.