Many species of animal age very slowly, and some so slowly that researchers have not yet been able to pin down either a rate of aging or a life span absent predation and accident. Some of those species might not age at all, but we'll have to wait for researchers to establish whether or not this is the case. Take the lobster, for example. Despite all the eating and farming that takes place, there's less funding for basic research into lobster biology than you might expect. As a consequence:

To date, there is no proven method to determine the exact age of a lobster. ... as best scientists can tell, lobsters age so gracefully they show no measurable signs of aging: no loss of appetite, no change in metabolism, no loss of reproductive urge or ability, no decline in strength or health. Lobsters, when they die, seem to die from external causes. They get fished by humans, eaten by seals, wasted by parasites, but they don't seem to die from within. Of course, no one really knows how the average lobster dies. There are no definitive studies.

Turning to another common sea creature, species of sea urchin appear to be in the same boat as the lobster: if they're aging, they're doing it very slowly.

The red sea urchin Strongylocentrotus franciscanus is a long-lived species and may live in excess of 100 years based on tagging studies in the field and corroboration from radiocarbon analyses as reported in the literature. Size-specific survival estimates reported here show no change in annual survival probability across the 6 largest 0.5cm size classes from 14.6 to 18.1cm. In addition to no change in survival probability there is no reduction in reproductive capacity with size. Red sea urchins show no evidence of senescence and so do not fit well within the context of the disposable soma theory of the evolution of longevity.

You'll recall that a baseline definition for aging is an increase in mortality rate with time, which doesn't happen for these urchins, or at least to any degree that can be detected via study methods at the present level of funding. This presents a challenge for the classic interpretation of the evolution of aging, which suggests that putting more resources towards tissue repair and the upkeep of biological systems that can support extended life spans is a losing proposition. Evolution favors the quick win, a fast and efficient organism that can reproduce quickly - and rapidly fall apart afterwards.

Or so the thinking goes. Clearly, extremely long-lived and possibly ageless species did evolve, so theory must be extended. The latest thinking on the matter theorizes that crowding can lead to a runaway evolutionary competition for longer lives, an arms-race for the biology that lets you wait out the competition for limited space:

adults live in crowded but stable conditions in which new opportunities for maturation arise rarely. In such situations, it behooves an individual organism to outlive its neighbors, so that when they die its seedlings or larvae have a place to dig in and grow up.

Does the humble urchin have any relevance to the future of human aging and longevity medicine? Not directly, I'd imagine, in the sense of applying learned science. But as more people understand the range of what is possible in living organisms, support for engineering a better healthy life span in our species will grow, whether or not that goal is achieved by mining nature for new metabolic biotechnology.