Many lower animals are capable of regenerating from near any injury, and in some species researchers struggle to find any signs that they are subject to degenerative aging. These are not complex creatures, however. Lacking a central nervous system or a brain and other complex organs implies the ability to be resilient and regrow tissues to a degree that a complex organism simply cannot match. This point was raised in comments on the possible agelessness of hydra, but there are other similar lower animals:
Hydractinia echinata has the power to regenerate any lost body part, can clone itself, does not age biologically, [and] "in theory - lives forever. Hydractinia has some stem cells which remain at an embryonic-like stage throughout its life. It sounds gruesome, but if it has its head bitten off, it simply grows another one within a few days using its embryonic or 'pluripotent' stem cells. So the potential for research is immense."
[Researchers have] discovered an unknown link between 'heat-shock' proteins and a cell-signalling pathway, known as Wnt signalling, in Hydractinia stem cells. "These two cellular signalling mechanisms are known to play important roles in development and disease, so they have been widely, though separately, studied. We have shown that they talk to each other, providing a new perspective for all scientists in this field. We found the link coincidentally - we weren't looking for it." Both the heat-shock proteins and Wnt signalling are known to be associated with cancer and cell growth. Hydractinia stem cells should be "very similar to their human counterparts and studying them may provide information on human stem cells."
"So why don't humans keep their pluripotent cells as adults? It's a good question. Keeping them in a complex body like ours is probably too dangerous, as they can easily form cancer. It's not so much a problem in simple animals - they would probably cut a cancer off. The price to become complex is to lose the ability to be immortal."
The great difference between a simple and a complex organism means that there may be little beyond knowledge to be extracted from these studies. We have evolved to lose regenerative capacity for reasons that probably have to do with the complexity of our structure - researchers can't simply port over the biology of lower animals to let our stem cells run rampant and expect positive results to follow. Improving human regeneration is something that will have to be carefully steered and controlled, as is the case in research presently taking place in the stem cell scientific community.