Immortality has a specific meaning here, which is that risk of death due to intrinsic causes does not increase over time. This is distinct from negligible senescence, which is more a case of few manifestations of aging until very late life.

Immortality seems to be the case for hydra, for example. (http://www.ncbi.nlm.nih.gov/pubmed/22689361)

Immortality is also observed for flies in late life (http://discovermagazine.com/2001/may/breakdialogue). They have a very high mortality rate at that point, but it doesn't increase further over time. That doesn't seem to be the case for humans, though, based on the very sparse data for people at extreme old age.

Human cancer cells are another interesting example besides hydras.