Anatta

A parable is given in the Pali Stanzas of the Sister Elders. There was a mother, we read, who had lost six children: one remained, a daughter. But eventually this child too died, and the mother was disconsolate. The Buddha came to her; and he said: "Many hundreds of children have we buried, you and I, hosts of kindred, in the times that are gone. Do not lament for this dear little daughter; four and eighty thousand with the same name have been burned on the funeral pyre by you before. Which among them is the one whom you mourn?".

- Heinrich Zimmer, Philosophies of India.

It seems highly improbable that any one individual could have had scores of thousands of children with the same name, even if they had lived thousands of lives. And regressing only a few hundred lifetimes, one would reach a prehistoric period in which the name did not even exist. So the sense received from the Buddha's words is that "you and I" - the woman, himself, all beings that are and ever were - are the immortal, universal Self who has lived all lives, borne and lost all children. 

One of the central teachings of Buddhism is the concept of anatta (non-existence of self); which is often interpreted to mean not only that individual egos are an illusion, but that there is no universal Self either - all is void of being (sunyata). However, this story suggests that the Buddha did believe in the universal Self  described in the Upanishads. Though believe is the wrong word - He knew.

(painting by Waldmuller)