JWBH,
You MUST read Spiritual Machines by Ray Kurzweil. It's a good book that describe a possible progression along the lines of what you're asking.
It asks a good question but I'll put it in my own words.
Let's say you have Joe. Joe blows his knees out and gets mechanical or artificial knees. Later as he grows older his eyes begin to fail and corneal inplants allow him to see. Same with ears, cochlear implants. Unfortuantely he loses his arms and legs in a car accident which are relaced with mechanical or organic replicas. He has a heart attack. Major blockage. He is given an artificial heart. Now he's really old and his liver and lungs, etc., are all failing. He is given replacements. Since he's aging, his memory begins to fail and he's given shunts placed in his cerebral cortex that bring back memories vividly. Even ones he wanted to forget. The year is now 2150 and his mechanical parts are failing along with his brain since he's now 180 years old. An advanced MRI takes a snapshot of his neural net and Joe's net goes into a fresh body (possibly grown from his own genetic material).
Now many of these technologies are in place as I write this and many are rapidly on the way. Here's the philosphical question: When does Joe stop being Joe. Or is he the same old Joe? What makes Joe "Joe"? After all, after the "neural transplant", Joe's in his new body has all his likes, dislikes, loves, etc.
Trust me, you'd enjoy the book better than my crappy interpretation.