There are no immortal porpoises, but Ebonmuse informs me that there are immortal jellyfish! Meet turritopsis nutricula:
So yeah, this shiny little number starts its life as a polyp, the juvenile form common to most hydrozoans and almost all cnidarians. These polyps are spawned in colonies of eggs, from which they hatch after just two days, then mature in two weeks to a month. But after spawning, rather than dying as most jellyfish do, our friend turritopsis does something different.
It turns back into a polyp. Then it grows back up into a medusa. Then it turns back into a polyp.
We have not found a way to stop them from doing this, barring some removal of the nervous system from the body proper. Unless you break or dismantle it, it lives forever, to the best of our ability to tell. I, for one, buy into Dr. Dawkins' idea that individual death may be valuable at the species level because "obsolete models" are given an intrinsic expiration date, so that the genes keep on shuffling. That's a gross oversimplification, but it makes intuitive sense to me and Dawkins makes a good case for it in The Selfish Gene, I believe. While individual death may or may not be valuable to a species in the long run (I'm sure there are ways of checking, though it seems like it would be really tough to test both rigorously and ethically), this jellyfish demonstrates that individual mortality is biologically optional.