Aging can be defined as a rise over time in mortality rate due to intrinsic causes. This doesn't tell us much about what exactly might be happening under the hood, beyond a general failure in function, but it has proven to be a useful working definition for a broad range of research. Not all species exhibit this rise in mortality rate, however:
Not all species weaken and become more likely to die as they age. Some species get stronger and less likely to die with age, while others are not affected by age at all. Increasing weakness with age is not a law of nature. [Researchers] have studied ageing in 46 very different species including mammals, plants, fungi and algae, and they surprisingly find that there is a huge diversity in how different organisms age. Some become weaker with age - this applies to e.g. humans, other mammals, and birds; others become stronger with age - this applies to e.g. tortoises and certain trees, and others become neither weaker nor stronger - this applies to e.g. Hydra, a freshwater polyp.
While there is plenty of scientific data on ageing in mammals and birds, there is only sparse and incomplete data on ageing in other groups of vertebrates, and most invertebrates, plants, algae, and fungi. For several species mortality increases with age - as expected by evolutionary scientists. This pattern is seen in most mammal species including humans and killer whales, but also in invertebrates like water fleas. However, other species experience a decrease in mortality as they age, and in some cases mortality drops all the way up to death. This applies to species like the desert tortoise (Gopherus agassizii) which experiences the highest mortality early on in life and a steadily declining mortality as it ages. Many plant species, e.g. the white mangrove tree (Avicennia marina) follow the same pattern.
Amazingly, there are also species that have constant mortality and remain unaffected by the ageing process. This is most striking in the freshwater polyp Hydra magnipapillata which has constant low mortality. In fact, in lab conditions, it has such a low risk of dying at any time in its life that it is effectively immortal. "Extrapolation from laboratory data show that even after 1400 years five per cent of a hydra population kept in these conditions would still be alive."