The tiny fresh water polyp Hydra does not show any signs of aging and is potentially immortal. There is a rather simple biological explanation for this : these animals exclusively reproduce by budding rather than by mating.
A prerequisite for such vegetative-only reproduction is that each polypcontains stem cells capable of continuous proliferation. Due to its immortality, Hydra has been the subject of many studies regarding aging processes for several years…
Kiel University : http://www.uni-kiel.de/aktuell/pm/2012/2012-332-foxogen-e.shtml