"Between you and I..." is wrong.

A British reporter once asked Sarah Ferguson, the Dutchess of Kent, how her daughter fared on the ski slopes and she replied, "between you and I, my daughter's an awful skier." I felt like I could hear poor Queen Elizabeth faint dead away, not because of her granddaughter's embarrassing lack of alpine skills, but because Fergie had stumbled over one of the most common misuses of the English language.

In all candor, I never really paid attention when my English teachers spoke about subjects and objects, but I did gather a sense for what was wrong simply from hearing it done frequently enough. Here's a refresher.

When a person performs an action, the personal pronoun describing them is the subject:

I talk to...
You talk to...
He talks to...
She talks to...
We talk to...
You talk to...
They talk to...

When the action is being done to a person or thing, their personal pronoun becomes the object:

... talk to me
... talk to you
... talk to him
... talk to her
... talk to us
... talk to you
... talk to them

This is why it is correct to say, "I talk to him", but not, "Me talk to he".

Say you have two people, Jim and Mary, standing on either side of a tree. Jim says to Mary, "The tree is between us." The tree is the subject, while Jim and Mary are the objects ("us"). Jim can also say, "The tree is between you and me," because "you" and "me" are personal pronouns used as objects.

Now, instead of a tree, imagine it's a secret: "let's keep this secret between us." This sounds correct, right? That's why it's also correct to keep the secret "between you and me."

Here are some other correct iterations:

You and I are next to the tree.
We are next to the tree.
The tree is next to us.
The tree is next to you and me.
The tree is next to them.
They are next to the tree.
Between us, he's a nobhead.
Between you, me, and the tree, there is no spoon.
Between you and me, if you make this mistake again, you are a nobhead.

And here's a detailed explanation about the surprisingly common object/subject confusion:

In the old days when people studied traditional grammar, we could simply say, “The first person singular pronoun is “I” when it’s a subject and “me” when it’s an object,” but now few people know what that means. Let’s see if we can apply some common sense here. The misuse of “I” and “myself” for “me” is caused by nervousness about “me.” Educated people know that “Jim and me is goin’ down to slop the hogs,” is not elegant speech, not “correct.” It should be “Jim and I” because if I were slopping the hogs alone I would never say “Me is going. . . .” If you refer to yourself first, the same rule applies: It’s not “Me and Jim are going” but “I and Jim are going.”

So far so good. But the notion that there is something wrong with “me” leads people to overcorrect and avoid it where it is perfectly appropriate. People will say “The document had to be signed by both Susan and I” when the correct statement would be, “The document had to be signed by both Susan and me.” Trying even harder to avoid the lowly “me,” many people will substitute “myself,” as in “The suspect uttered epithets at Officer O’Leary and myself.”

“Myself” is no better than “I” as an object. “Myself” is not a sort of all-purpose intensive form of “me” or “I.” Use “myself” only when you have used “I” earlier in the same sentence: “I am not particularly fond of goat cheese myself.” “I kept half the loot for myself.” All this confusion can easily be avoided if you just remove the second party from the sentences where you feel tempted to use “myself” as an object or feel nervous about “me.” You wouldn’t say, “The IRS sent the refund check to I,” so you shouldn’t say “The IRS sent the refund check to my wife and I” either. And you shouldn’t say “to my wife and myself.” The only correct way to say this is, “The IRS sent the refund check to my wife and me.” Still sounds too casual? Get over it.

On a related point, those who continue to announce “It is I” have traditional grammatical correctness on their side, but they are vastly outnumbered by those who proudly boast “it’s me!” There’s not much that can be done about this now. Similarly, if a caller asks for Susan and Susan answers “This is she,” her somewhat antiquated correctness is likely to startle the questioner into confusion.—Source