Most of your tissues are in a constant state of flux, the cells within a mix of those destroying themselves after dividing too many times, those dividing to create new cells to make up the numbers, and a smaller flow of fresh cells with many divisions remaining that are created by a small population of stem cells. Some tissues turn over their cell populations very rapidly, such as blood or the lining of the gut. Others consist largely of cells that will last as long as you live, such as much of the central nervous system. In all these cases, however, an embedded population of stem cells supports continued maintenance and function. If stripped of stem cells you would crumble into premature death in perhaps a decade or so.

That said, aging is effectively a process of being stripped of stem cells in addition to all of its other detrimental consequences. The maintenance of tissues diminishes degree by degree with the years until organs and systems fail, eventually fatally. Modern research suggests that, for those tissues where there is good data, the stem cells are still largely present, however. They have simply relinquished their jobs, lapsing into lasting quiescence or senescence in response to rising levels of damage. This set of affairs most likely evolved as a cancer suppression mechanism, our natural life span a balance between risk of death by tissue failure versus risk of death by over-active damaged cells spawning a cancer.

Experiments in moving stem cells between young and old tissue environments suggest that most types of old stem cells examined to date are quite ready to get back to work - and even do their jobs effectively despite their age - if only the signals present in their environment instructed them to do so. It is expected that if one could wave a wand in old humans and restore stem cells in all tissues to youthful activity, the result would be a lot of cancer in addition to improved tissue maintenance, however. Still, temporarily altering specific signals to boost stem cell activity has great potential as a therapy for the near future, with raised risk of cancer compensated for by an increasing effectiveness in cancer detection and treatment. First generation stem cell transplants are in effect a way of making native cells do more than they would otherwise have done by adjusting the balance of signals in the affected tissues. In years ahead more sophisticated methods will be used to achieve better and more controlled results in the same vein.

Ultimately the goal of rejuvenation by repair of cellular and molecular damage will hopefully automatically lead to restoration of stem cell activities. If the damage goes away, so too should the signaling environment that is a response to that damage.

Here is a readable review paper on stem cells present in adult tissues and their relationship to aging. There is a lot of detail packed in there, so take a look at the whole thing:

Adult Stem Cells and Diseases of Aging