In Song of Myself by Whitman, who is the "you"?

Well, when Whitman says you, he means you, as in, "You there, holding the book, reading these words." That would seem to be the case, at least, for most of the poem -- when he says, "And what I assume you shall assume," the power of the line comes from Whitman's direct address to the reader. Except, there is another sense in which the "you" can be understood as the poet's soul, and that the...

Well, when Whitman says you, he means you, as in, "You there, holding the book, reading these words." That would seem to be the case, at least, for most of the poem -- when he says, "And what I assume you shall assume," the power of the line comes from Whitman's direct address to the reader. Except, there is another sense in which the "you" can be understood as the poet's soul, and that the whole poem might better be known as "Song to Myself." The reference to "soul" becomes explicit in section five:

I believe in you my soul, the other I am must not abase itself to you,  
And you must not be abased to the other.  
Loafe with me on the grass, loose the stop from your throat,  

Not words, not music or rhyme I want, not custom or lecture, not even the best,  
Only the lull I like, the hum of your valved voice.

Whitman posits here a duality between the soul and its "other," which, presumably, is the poet's fleshly body. The "you" clearly references the "soul," that is, the poet himself. His fascination with his soul's "valved voice" takes an auto-erotic turn in the next lines:

I mind how once we lay such a transparent summer morning,  
How you settled your head athwart my hips and gently turn'd over upon me,  
And parted the shirt from my bosom-bone, and plunged your tongue       to my bare-stript heart,  
And reach'd till you felt my beard, and reach'd till you held my feet.

The personification of the poet's soul -- its transformation into a lover -- is characteristic of the way Whitman thinks of of the second person -- which is, in short, that there is no second person, only one great, encompassing first person. So when Whitman says "you," he does mean you, but he also means himself, and potentially, every one else.