There probably isn’t a really good answer to this since when a cell divides it is impossible to say which cell is the original, but to what extent has your body replaced your cells by the time you have reached adulthood? IOW, I expect that the skin I had when I was 10 has long since flaked off and been replaced by new tissue. To what extent is this true for other organs, especially the central nervous system?
I can’t even begin to answer this question myself, but I was curious and did a little googling. I found a few hits with keywords like atom, cell, turnover, and human. I don’t know how accurate this information is, but maybe it’s a starting point.
I’ve done a little more searching and I found a WikiAnswers that addresses this question: Does the human body regenerate every 7 years?, and it references a newer study that found:
I don’t think neurons die, they just replace their atoms.
And as for tatoos - maybe they dye the cells that are actually doing the dividing? I’ll guess that since those cells shouldn’t die, the ink probably can’t leave the cells. Or maybe it stains the connective tissue and cannot leave that area.