Then you have the crowd who have an inkling they may not be able to choose correctly between the nominative and objective versions of the pronouns and think they can circumvent it entirely by using the reflexive pronoun 'myself' instead. Doesn't work like that!

That said, 'me' has generally been crowding out 'I' for a long time in many circumstances. Who, me? Yes you! Me too...

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And there's such an easy way to get it right every time. Just eliminate the other subject in the sentence and use that to judge whether "me" or "I" should be used. The same answer applies when the other subject is included. Definitely a pet peeve of mine when this simple rule is not followed.

"I went to the store" has the same usage as "My wife and I went to the store".

"My mother gave me a present" is the same usage as "My mother gave my wife and me a present".