Yes: exactly like the Elves of Tolkien’s Lord of Rings, on our real Earth, there are living beings that never age and are examples of biological immortality!
The most common and cited example of these creatures are hydras. Hydras are small, simple, fresh-water predators which can be found in most unpolluted ponds, lakes and streams in the temperate and tropical regions: you just need to gently sweep a collecting net through weedy areas. They have a tubular body up to 10 mm long when extended, secured by a simple adhesive foot called the basal disc.
All their cells continually reproduce by division (mitosis), and this allows defects and toxins to be diluted. Daniel Martínez, from the Department of Biology of the Pomona College in Claremont, California, wrote an article where he suggests that hydras do not undergo senescence and, as such, are biologically immortal.
Exactly like the immortal Elves in the Lord of Rings, they can be killed but, in absence of external nuisances – such as diseases or injuries – they would continue to live.
Also planarian flatworms are common to many parts of the world, living in both saltwater and freshwater ponds and rivers. Some species are terrestrial and can be found under logs, in the soil and on plants in humid areas. Some of them exhibit an extraordinary ability to regenerate lost body parts and appear to exhibit an ability to live indefinitely.
The scientific explanation
Australian-American biological researcher, Prof. Elizabeth Blackburn, 2009 Nobel Prize in Physiology or Medicine with Carol W. Greider and Jack W. Szostak, published an article in 1978 about her discovery: telomeres.
The simplest way to describe telomeres is to imagine a chemical “protection” at the extremities of the chromosomes in the DNA. Without them, the chromosome itself and the genetic information it holds would be deteriorated during the normal biological processes. Telomeres are disposable buffers: they are consumed during cell division and are replenished by an enzyme called telomerase reverse transcriptase. But this repair is not perfect and, unfortunately, over time, due to each cell division, the telomere ends become shorter.
We could think of senescence as the worsening of the biological processes such as the cells reproduction (mitosis), up to the point that these process don’t happen anymore and the individual dies.
Well: hydras and planarian flatworms manage to maintain the length of their telomeres and seem to protect indefinitely their DNA. They don’t age and they would only die by injury or poison.