Instead, the Buddha explains the perceived continuity of the human personality by describing it as composed of five attributes (skandhas) none of which contain a permanent entity.
> As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true & established, or else he has a view like this: This very self of mine — the knower that is sensitive here & there to the ripening of good & bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will stay just as it is for eternity. This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.
So while it is important to continue to examine things to realize that each thing under examination isn't a self, isn't me, isn't mine, isn't unchanging, isn't eternal, that doesn't mean that there is a doctrine that there is no self. The Buddha explicitly refuses to answer the question of the existence of a self, and says that to hold either of the views "there is a self" or "there is no self" is unskillful, a fetter, an impediment to freedom.
cf "Selves & Not-self: The Buddhist Teaching on Anatta, Thanissaro Bhikkhu" http://www.accesstoinsight.org/lib/authors/thanissaro/selves...
edit: I looked this up and now I'm more confused than when I started. There is a distinction made between the lowercase self and capital Self all right; I'm just not sure I understand the details.
The human "Self" -- capital S -- generally refers to Atman. Atman is a "shard" of Brahman. So Self does denote Brahman, but with the tacit understanding that Atman is itself composed of Brahman, like a small patch of a flowing stream. It's not its own separate entity, but rather a piece of the whole that is also representative of the whole (look up "Tat Tvam Asi" for more on this concept).
The self -- lowercase s -- is generally used to refer to the dual self that humans have: Atman and Jiva. The Atman is the Self as we discussed before (but the Self is also the divine, as Krishna claims throughout the Gita). The Jiva, however, is the discrete part of the self -- the ego, all wants/desires, attachments to sense-objects and the physical world. When in casual conversation we discuss ourselves, a Hindu would likely claim that we are in fact discussing the Jiva.