So, I was talking to Ryan the other day and he made some crack about my last grammar-centric post and then begged me to clarify the I/me confusion rampant in the world. So, here goes:

Once upon a time, English was born. Its parents were Germanic, and so was English. Now, it is a long-standing tradition in the Germanic family to mark case¹ but English was a lazy child, prone to frolic with languages from many distant lands, steal their vocabulary, and forget all the wonderfully complex rules that he² was taught at home. One of the rules that English liked to skimp on was that of case-marking.

Now, let's discuss a very simple sentence that is often referred to in linguistic textbooks:
The dog bit the cat.

Tell me, who bit whom³? You, because you are familiar with English, know that the dog did the biting and the cat was bitten. However, there is nothing inherent in the words to indicate that. This is because we indicate nominative (the biter) by putting it before the verb, and the accusative (the bitten) by putting it after the verb. In German, on the other hand, order is not so important as the preposition, which is marked with case. Observe:
Der Hund beißt den Mann. The dog bites the man.
Den Mann beißt der Hund. The dog bites the man.

So, you can see that "der" indicates nominative and "den" indicates accusative. Whether "der Hund" appears before or after "den Mann", "der Hund" is biting rather than being bitten.

English used to work this way too, and we have a remnant of this case marking on our pronouns:
1st person singular: I (Nominative), Me (Accusative)
2nd person: You (case is lost here)
3rd person masculine singular: He (Nominative), Him (Accusative)
3rd person feminine singular: She (Nominative), Her (Accusative)
1st person plural: We
2nd person plural: You
3rd person plural: They

Now, on to Ryan's pet peeve. It is commonly said that one should never say "Michelle and me," but "Michelle and I." This is true in certain linguistic situations. If Michelle and yourself are performing the action in the verb (for example, biting), then you should go with "Michelle and I" because "I" is nominative and you are doing the biting. However, if Michelle and yourself are having the action done to you, then "I" would be erroneous, and "me" would be correct. So:
Michelle and I bit into our apples. (GOOD)
A boy started talking to Michelle and me. (ALSO GOOD)⁴
*⁵Michelle and me thought he was pretty cute. (NO!)
*He tried to borrow an apple from Michelle and I. (NO!)

If you get confused, think of it these simple examples:
I saw you. (good)
*Me saw you. (bad!!)
You saw me. (good)
*You saw I. (bad!!)

Now, my dear readers, go forth and sin no more.

1. Nominative/accusative in this family, we'll have none of that absolutive/ergative nonsense here!
2. Ask any feminist—English is male.
3. Yes, keeners, good for noticing: 'who' is nominative, and 'whom' is accusative. So, "who are you?" is good because the 'who' stands for the 'I' in the answer ("I am some random grammar-obsessed girl"), and "whom did you speak with?" is good because 'whom' stands for the accusative someone in the answer ("I spoke with Ryan"). However, "*whom are you?" and "*who did you speak with?" will get you kicked in the balls by a grammar queen, so if you're going to dare, you should either be a) female, or b) crossing your legs.
4. Compare: "A boy started talking to me." and recall the previous entry on adjuncts.
5. In linguistics, anything that is prefaced by a * is wrong, bad, or impossible.