The thing here, is that this is the one grammar point every native speaker has been taught to hear as wrong. Everyone in school had a teacher who would say "MIKE and I" emphatically if "Mike and me" or "Me and Mike" was said in conversation. GRAMMATICALLY SPEAKING is it wrong? Depends who you ask. Take for example this question: "Who is hungry?" ANSWER: ME. Did everyone hear that, I asked who is hungry? Who is hungry here? : ANSWER: MY FRIEND. However, we have all been taught to say MY FRIEND AND I so much, that people inherently think it is wrong. EVEN with Judy's example of a prepositional phrase He bought gifts for my friend and me, I still hear my 3rd grade teacher saying "He bought gifts for my friend and I." Judy is right, but if you can't decide, go with my friend and I. and if you start a sentence with this as the SUBJECT, then for sure use it. "My friend and I are ...." . Me and my friend, is to be avoided and all costs.