Unfortunately, there's one I can't keep to myself anymore. In the past few weeks alone, I have heard approximately 4 billion* I/me errors. These aren't just being made by non-writer family members and friends. I've heard lines like "he gave it to her and I" on TV shows, seen them written in magazines, and horror of all horrors, even found one in a published novel.
This error is rampant in popular music, too. Lady Gaga alone has not one, but two major hits that prominently feature I/me errors. In the song "You and I," there's the line "Yeah, something about, baby, you and I." The song "Bad Romance" has this lovely gem: "You and me could write a bad romance."
Rule #1: Use "I" for the subject of the sentence (the person who's performing the action).
This is why we say I went to the store rather than Me went to the store. If there's more than one person performing the action, that's okay--you should still use "I" (as in Tony and I went to the store).
The only place where this rule gets tricky is when a word acting as a subject in the sentence isn't at the beginning. For example, if you were to say This is the one I like, it's correct to use "I" instead of "me" because "I" is doing something (in this case, liking).
Rule #2: Use "me" when the action of the verb is being done to the person.
This could be a straightforward sentence like My sister hit me or a more complicated one like Lucy wrote an email that she forwarded to Jackie and me. (Notice that in the last example, "me" is the object of a preposition. In this case, you would always use "me" instead of "I.")
Again, the sentence order could be switched around so you end up with "me" at the beginning. In the sentence Between you and me, this isn't a good idea, the correct word to use is "me" because it's the object of the preposition "between."
Quick and Very Useful Tip: Most of the confusion comes from instances where the "I" or "me" is connected to another pronoun or name. Example: He told the good news to her and (I or me?)
When you encounter a sentence like this and aren't sure which one to use, try writing or saying the sentence without the first pronoun and the conjunction. So for this example, the choices would become He told the good news to I or He told the good news to me.
It's pretty easy to hear that "me" would be correct, isn't it?
If you're more confused than before, or if you're looking for a more in-depth discussion of I/me errors, try the following links:
Grammar Girl: Between You and Me
Oxford Dictionaries: "I" or "me"?
WikiHow: How to Choose Between "I" and "Me"
*This is a slight exaggeration. It was probably more like 3.8 billion.