There's confusion when it comes to the difference between me and I. For example, we say Not I, but Woe is me; John and I went to the shop, but Sam gave John and me a book. Which pronoun do we use, and when?
Let's start with the easiest first. In the last example, Sam gave John and me a book, the pronoun me takes the dative case, meaning that an action is given to someone or something. We use me for the objective case as well: Sam took John and me to the bookstore. Again the subject is Sam, not me. If all this is too damn complicated, I have a tip: take out the unnecessary character and see what makes sense. Sam took I to the store or Sam took me to the store. This trick also works with the third example. John and I went to the shop becomes I went to the shop.
Who killed Cock Robin? It is I. In this example, it is is a transitive, or linking, verb. No action occurs, and an old rule is that subject pronouns follow these verbs (I, he, we). This also applies to the negative answer: not I. Of course, in modern colloquial usage, few speak like this, and you'd be better off being wrong and fitting in than being right and sounding like a Shakespearean nobleman: Who ate my waffles? Not me. Wasn't me. T'was I, Lord of Grammar and Judgment.
Woe is me does not follow the same convention, and that's because it takes the dative case—there was a reason I mentioned this case earlier. We can rewrite the phrase to woe is given to me. Now we see that me takes the dative case, not subjective case.
For one final example, I will reference Mary Norris from The New Yorker magazine. Let's take the following example: John is a better athlete than me. A lot of people would argue that it should read, John is a better athlete than I, with a silent am hidden at the end. I would be one of those people. But Mary Norris instead argues that the me is correct because than works as a preposition, not as a conjunction, and since a preposition takes the objective case, me is correct. You can watch her argument here.