There’s a species of jellyfish that never dies. Known as T. dohrnii, and colloquially as the immortal jellyfish, the species can indefinitely revert between its mature and larval forms. It’s not immortal, per se — it can still be eaten, be killed, or succumb to disease. But if left unchecked, it could live forever.
It’s one of the only things that can. There are some plants and bacteria that seem immortal, and some animals that live for a very long time, but most everything else ages. Especially animals. Over time, our bodies accumulate damage. Being alive takes a lot of energy, and there’s bound to be some collateral damage.