There are many organisms that appear to be able to live for exceedingly long times (and perhaps indefinitely). Disregarding unicellular organisms, there are, for example, species of jellyfish that appear biologically immortal [1]. There are also examples of trees (or, rather, root systems) that have lived for extremely long times [2].
https://en.wikipedia.org/wiki/Greenland_shark
"The oldest of the animals sampled, which also was the largest, had lived for 392 ± 120 years and was consequently born between 1504 and 1744"
Listed here though:
https://en.wikipedia.org/wiki/List_of_longest-living_organis...