Religion
In reply to the discussion: Dawkins and Pell battle it out in one hell of a debate [View all]there is no working definition of what to measure to begin with, so what's the point of making claims of that undefined unmeasurable ceasing or continuing?
Also the position of agnosticism not denying that something may be possible (which would be claim of impossibility or active disbelief) does not need to define a mechanism for potential possibility. There is lot of middleground between impossible and positively proven/probable.
As for evidence that you are so interested in, what comes first to mind are clinically brain dead patient (brain frozen for duration of surgical operation) having recollections of the events during the operation that were verified by the medical staff present, telepathy, memories and physical marks of other lives, etc.