Which is correct, "you and I" or "you and me"?

When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I".

This is an example of hypercorrection, which is when native speakers make an accidental error in their zeal to avoid a different error.

In this case, the error that's being avoided is the error of writing "you and me" in subject position, as in the following sentence:

You and me are going to the store.

This is formally incorrect, although it's very common in contemporary spoken English. Because they have been taught that this is incorrect, many people hypercorrect and change "you and me" to "you and I" in all positions. That is, they incorrectly learn the rule about when to use "you and I", and so produce sentences like the following:

You and I are going to the store. [Correct]

He'll come to the store with you and I. [Incorrect]

"You and I" is the subject. "You and me" is the object.

"You and I hate Phil." "Phil hates you and me." "Phil is hated by you and me." All of these are grammatically correct. (No offence to Phil.)

It really winds me up when people hypercorrect because they think that "you and me" is always wrong. "Phil hates you and I." NO! This is worrying.

The best way to work out if you should be using "you and I" or "you and me" is to take away the "you and" and see if the sentence sounds right with just I or me.

"I hate Phil." Sounds good. "Me hate Phil." Sounds like a caveman talking!

"Phil hates me." Sounds good. "Phil hates I." Sounds ridiculous!

They are synonymous but grammatically different. They are often used interchangeably (incorrectly) by native speakers. There is a simple way to tell which one to use, by imagining the clause without the "you and" part:

Example: You and (I/me?) should spend more time together
Imagine: "Me should..." (this is clearly wrong)
Imagine: "I should..." (correct!)
Answer: You and I should spend more time together

Example: He should have spoken to you and (I/me?).
Imagine: "He should have spoken to me" (correct!)
Imagine: "He should have spoken to I" (wrong)
Answer: He should have spoken to you and me.

An alternative view is that "you and me" was always OK until somebody decided in the 18th century that English should be like Latin and started teaching that you have to use 'I' when you would use 'ego' in Latin. Since the rule taught since then is hard for English speakers to grasp (since grammatical case is marginal in English), many people are unsure of where to apply it, hence the hypercorrection. In fact, in Joseph Emonds' 1985 paper "A grammatically deviant prestige construction" he shows that there are slightly more complicated examples (which I cannot recall to mind) where even people who think they do know the rule are often unsure. His paper argues that English with that rule is not a possible natural language, in the sense that there is not enough information about case available to an English-speaking child to construct the rule. His claim is that the rule exists only as a rule learnt in school or equivalent.

There are three styles of using "you and I" or "you and me". For each I will give two example sentences - the first with "you and I/me" as the subject and the second with "you and I/me" as the object.

Style 1: You and me beat him. He hates you and me.

This is normal English as learned by many children, found in prose and dialogue in works of the best authors, and taught to learners of English as a second language. I is of course the normal subject pronoun and me is the normal object pronoun. But in this style, me is also an emphatic variant of I that is used (among other uses) whenever several nouns or pronouns are joined into a single subject or object. This is the most correct style in the sense that it is how educated normal people normally speak.

I guess that some French influence was at work in the formation of this grammatical phenomenon, since alternation between French je (I) and moi (me) follows very similar patterns.

Style 2: You and I are reading the book. He is attending the course along with you and me.

This is formal, high-prestige English as taught to native English speakers who want to improve their language to advance in society. It is the most correct style in the sense that it has the highest prestige. But it is not how people normally speak, and most children even in educated families do not learn this style naturally.

This style is similar to how other Germanic languages work naturally, and very different from French.

Style 3: You and I should go to the party. She wants to meet you and I.

This is the hypercorrection that logically results when someone is taught style 2 but doesn't really understand it beyond "'you and me' is sometimes (hypercorrected to: always) wrong". As much as I hate to admit the fact, this style is so common that it is arguably correct. We can even justify this by arguing that in style 1, the case information gets lost when two subjects or objects are joined, and then using subject case is pretty logical unless we specifically want the emphatic variant to emphasise the first person.

This pattern is unlike any other language I know, at least among those that distinguish subject and object case for pronouns. In particular, it doesn't exist in French because French speakers are not taught to think of their version of style 1 as wrong, and it doesn't exist in German because style 1 is just plain wrong in German and every native German speaker grows up with style 2. (So both French speakers and German speakers have no reason for this type of hypercorrection.)