[kweingar]

I strongly encourage you to read the later chapters of Derek Parfit's Reasons and Persons. It is entirely dedicated to the question of personal identity, or more accurately, what "matters" when it comes to personal identity.

He doesn't really address the question of reincarnation specifically, but I think you would still find it interesting. He challenges typical notions of personhood ("What makes me different from you is the physical continuity of my body over time") by pointing out that this is only a technological limitation. We could imagine a world with teleportation or brain transplants where this wouldn't necessarily be true.