Aging is near universal most likely because it provides considerable evolutionary advantages: aging species are more likely to survive changes in their environment, despite the fact that aging is a tremendous disadvantage from the perspective of the individual. The world changes, and so we and near all of our ancestors age and suffer. I did say near universal, however. The more primitive the types of organism surveyed, the more likely it is that you will see signs of agelessness: a few species of creature that, given sufficient peace, quiet, and nutrients, can repair themselves indefinitely.
Hydra may fall into this category, for example. When a species doesn't have a brain or any sort of very complex organ and configuration that is essential to the self, then aggressive regeneration is a viable strategy. That apparently stops being the case as complexity increases: there is some point at which evolution selects for a loss of regeneration in favor of ever more complicated structures. As a species we are a long, long way past that point. The most complex species capable of feats of complete regeneration of organs and limbs are small animals such as salamanders and zebrafish, and even they are nowhere near as good at it as the hydra.
Looking further down the tree of life, it was thought at one time that bacteria do not age. They do age, however, a fact uncovered not so very many years ago. Aging in bacteria is a matter of accumulating damaged materials and waste products, and the various strategies by which breakage and waste can be removed or diluted. Because the situation is comparatively simple it is possible for bacteria to stay ahead of aging just by dividing fast enough:
The team has shown that, unlike other species, the yeast microbe called S. pombe, is immune to aging when it is reproducing and under favourable growth conditions.
In general, even symmetrically diving microbes, do not split into two exactly identical halves. Detailed investigations revealed that there are mechanism in place that ensure that one half gets older, often defective, cell material, whereas the other half is equipped with new fully-functional material. So like humans microbes, in a sense, produce offspring that is younger than the parent.
But aging is not inevitable for the common yeast, S.pombe. The newly-published work shows that this microbe is immune to aging under certain conditions. When the yeast is treated well, it reproduces by splitting into two halves that both inherit their fair share of old cell material. "However, as both cells get only half of the damaged material, they are both younger than before". At least in a sense, the yeast is rejuvenated a bit, every time it reproduces.
We should not be surprised to see rejuvenation in practice in nature. All species are capable of rejuvenation: it's how old parents produce young children. Somewhere in that process is a step in which a lot of cleaning and repair takes place, prior to the point at which the embryo is too complex to support the necessary aggressive rejuvenation programs. If those same programs were turned on in an adult, the result probably wouldn't all that pretty. Lower species like hydra can get away with constant regeneration because it doesn't greatly inconvenience them to throw away or rebuild an entire section of an individual's body. We are only in that same boat for the very earliest period following conception.
Here's the scientific paper for the research mentioned above:
Many unicellular organisms age: as time passes, they divide more slowly and ultimately die. In budding yeast, asymmetric segregation of cellular damage results in aging mother cells and rejuvenated daughters. We hypothesize that the organisms in which this asymmetry is lacking, or can be modulated, may not undergo aging. We conclude that S. pombe does not age under favorable growth conditions, but does so under stress. This transition appears to be passive rather than active and results from the formation of a single large aggregate, which segregates asymmetrically at the subsequent cell division. We argue that this damage-induced asymmetric segregation has evolved to sacrifice some cells so that others may survive unscathed after severe environmental stresses.
This sort of research provides some insight into the very early evolutionary origins of degenerative aging, and as such it is interesting to follow even though there is nothing here that will greatly affect the course of programs aimed at producing human rejuvenation.