If Buddhism claims there is No Self, how can a person remember their past lives?

it could have something to do with the idea of an absolute and relative reality. The absolute reality of Buddhism is emptiness, and "no self" would fall into that. Ultimately, there is no self. But when you are living in the world, in one of these lives, your perception is that there is. I'm guessing that, that which perceives this separation, or your consciousness, extends back in time, so that a series of seemingly separate "selves" are connected together, giving you the series of lives that you will remember as "your" past lives. (in other words, your illusory self of separation in this current life is an extension of your illusory separate self in the last life, and lives before that. the unit of illusory separation did not stop at your deaths and births)

But now I wonder...If there ultimately is no self, despite the fact that people remember past lives as "their own," are all of those past lives your and everyone else's lives? In other words, do we all share all past lives, and are we all right now, each other's "past" (or current/simultaneous, or future) lives? (of course this is assuming that time is not linear...I think Buddhism says time is an illusion anyways...actually, everything is an illusion anways so I guess it really doesn't matter...)

This is one question you can not answer from reading about Buddhism or it's philosophies. If there is no self, best meditate on this. By the way, if you meditate on sounds or music you may hear the gaps between the notes.

im sure i knew the answer to that question at one time.

http://en.wikipedia.org/wiki/Rebirth_(Buddhism)

There is no permanent self. The self that is in everyone is one self. Each life represents a mortal self. Yet, even though everyone dies, our intelligence implies a supernatural phenomenon.

Shifting between the physical and metaphysical here, I could contend that past life memories are simply implants acquired after birth. I could also contend the since all atoms are recycled, there is a possibility that you DO have an atom or two in your body which once belonged to Cleopatra. (Theres a "Zen" thought for you) So if memory is atomic, then you may have a few "moments" that are genuine. However as a part of the universe, we all exist, always have and always will. (Using the same atomic theory) The goal is to get off the ride at Nirvana.