Let's say you're on your deathbed and this is a great deal in the future. A doctor has offered you two choices. 1. You die and 2. Your memories, thoughts, and emotions can be downloaded on a machine so that you can continue to live. If you choose the second one...are you really still alive?
I'd have to say no, because, we are talking about one's consciousness. I think a new consciousness would begin, and the old "you" would die. This is because, when you look at it, it's not a "transfer" but a destructive copy process. All the attributes of your consciousness are first
duplicated, then the original is
destroyed. You would see the machine whir to life from your bed, and then the lights would go out.
On a similar note - I wouldn't step onto a star-trek transporter either. I am pretty sure I'd "die" and a doppelganger would take my place at the other location. The copy would be sure the transporter worked, unable to tell it's consciousness only began that second, and decide they are entirely safe and don't interfere with the continuity of a conscious being's experience, but that would be an illusion.
That.... or all continuity of consciousness is an illusion - for all I know the individual life-cycle of consciousness only exists for a millisecond, or until one falls asleep... no way to know for sure. Not being able to know - I think I'd play it safe.
Another question: Your friend who saved your life once is dying, and gets cloned and has his consciousness transferred. Before the original is destroyed, someone busts into the room and says they have a cure that will let him live in perfect health, but with a 10% of relapse. You, him, his clone all go rock climbing, and due to an accident, you can save the original or the clone. Which do you save, and does it matter?