It doesn't matter to me. I would say 'my friend and me' rather than 'my friend and I' because it sounds better to me ... it is really just a question of taste. A lot of people get hung up about the 'correct' way of speaking .. with the idea that in some sense one formulation is 'right' and another is 'wrong'. Usually these people are ignorant of how language works in general, the actual syntactic and semantic properties of the words used, and their history. For example, in a conjunction like 'my friend and ...' no case is assigned to the individual words by the deep grammatical principles by which language actually does work .. which have to do with the computational systems in the mind-brain that underlie our linguistic capacities. So it is question of what form people happen to use as a default for the first-person pronoun: 'I' or 'me'. And both are widely used. I think 'me' is actually a more natural default form for English. So, for example, if someone is offering the last piece of cake and says 'who wants this?', the natural one-word answer would be 'me' and not 'I'. The elite would normally say 'my friend and I went to the opera' but 'Peter gave it to my friend and me' with the idea that the pronoun is a nominative position in the first example and a dative position in the second (as in 'I went to to the opera' and 'Peter gave it to me'). But actually it isn't, it is default in both. I would use 'me' in both instances. But many would use 'I' in both instances. It is just a matter of taste.
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I was recently at a wedding where one of the guests at my table (people from the other side of the new family) said something about the "maid of honors". Another person sitting next to him quickly leapt in to correct him into saying the "maids of honor," and I was then witness to a ten-minute, heated argument about whether or not it mattered. So that is my question to you, philosophers. How much does it matter whether a person makes minor grammatical mistakes, so long as everybody understands what is meant? How important is it to say "My friend and I" instead of "Me and my friend," or "Passers-by" instead of "Passer-bys"? What is at stake?