What is passed from life to life in the process of rebirth?

As a practising Buddhist, I am often asked this question: what is passed from life to life in the process of rebirth? I have several answers to this depending on my audience - e.g. lessons to be learned, experiences to be resolved or, simply, one's own personal cockpit-style 'black box' of all that has been seen, heard, experienced etc in previous lives. To what extent do colleagues believe that 'personality' or 'behavioural tendencies' should also be included? I welcome your views. My question is directed at any practitioner of Buddhism, Theravadan or otherwise.