We may debate about what the self "really" is, but take away the memories and that individual self is, to all intents and purposes, gone.
As always your posts are thought provoking Magister. This made me think about the concept of retaining the memories of an individual beyond what is currently possible by storing them in our brains.
At present it seems mostly to be in the domain of science fiction writers, but I recall some articles in Wired around the turn of the century that spoke of it as a future possibility that scientists think that they can figure out before the next century. To me that has much more interesting possibilities than thinking about who one was in a previous life.
For what it's worth I think that reincarnation as a concept serves two purposes which are more social/psychological.
For people with boring lives this offers an opportunity of adding some "spice" to their lives without the risk involved in actually doing something. Without any risk you can hear tales told to you about past lives (there are always people willing to do this - for a reasonable price
) which were much more interesting. Perhaps you were a general in the Roman army or the concubine of an emperor. Now your life is more interesting and you don't complain about your pathetic little life, since you are obviously just serving a temporary karmic sentence that will grant you something interesting in the next life.
The other purpose is in making a social contract, not seen much today in our advanced society, but something useful in the days when individual skills were needed to ensure the survival of a group of people. If you start out telling a person that he/she is the reincarnation of a great hunter or a skilled blacksmith they will (hopefully) start applying themselves to that task and in the end make a valuable contribution.
To me, that's the usefulness of reincarnation, not as a personal offer of hope, but as a tool to be used (or abused in some cases) to keep the social order or ensure personal gain.