I have always thought that the "you" that is addressed is the other self that J. Alfred Prufrock has been forced to create so that he can communicate and converse in a way that he is unable to do in reality. It fits that a man who shows himself so incapable of living in the real world must need to create another "self" or listener to confess to.
I always interpret it that he is speaking to the reader. It sort of ties in with the piece from The Inferno at the beginning of the poem--to paraphrase, if I thought you'd ever get out of here, I'd never tell you these things-- the way Eliot uses that, I believe, is directed towards the reader.
He invites us to come along with him and learn about his lonliness.
I find the "you" to be the distorted and disconnected consciousness of Modernism. Isn't it incredible that someone as young as Eliot could have penned a poem so nuanced with pain and regret? (He was only 29 when it was published.) There is so much beauty and angst in this poem. I have always loved the image of the cat, so full of love but separated by such transparent, yet solid, coldness.
For a poetry class in grad school, I memorized the entire poem by listening to Eliot read it (including the Latin!) in my car on the way to work. (It is on that marvelous colletion of a few years ago, "Poetry Speaks."
I cannot read the poem without hearing Eliot's voice. If anyone would like to hear it, please visit this link. The "frustration and irony" of the age come through so clearly in his inimitable tone. It is available through Salon.com. Harper's calls Eliot, "One of the great readers-aloud of this century."
http://www.salon.com/audio/2000/10/05/eliot/
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