There's a good conversation about this, humans and cell regeneration specifically, in the movie "Waking Life" (as well as many many other great conversations about a variety of philosophies)
yes, the fact that it applies to people makes it very interesting.
am i the same person as when i was born?
i would like to think that i am... but 'knowing' this makes me question a lot of the seemingly obvious things about self, to the point where i wonder exactly what i am, and realise that it is very poorly defined to start with... and probably not so special. :)
And applies to humans, too, with our continually regenerating cells.