Marine methuselahs
"Although this is an impressive lifespan for such an unassuming mollusc, many corals are probably much older. Off the island of Ta'u in American Samoa, in approximately 13m (40ft) of water, lives an enormous helmet-shaped coral at least 7m (22ft) high and 12m (37ft) in diameter. This coral, a colonial invertebrate in the scleractinian genus Porites, consists of at least 100 million polyps and is likely to be at least 600 years old. It may well be much older, given the fact that it began life in relatively deep water and therefore may have grown more slowly during its first few centuries. In fact, it's not inconceivable that it dates back as far as the fall of the Roman Empire or the birth of Christ. Chuck Birkeland and others at the University of Hawaii have studied this coral for some time, and have identified it as a candidate for the title of "world's largest coral".
The photo shows this coral, which I believe is affectionately nicknamed 'Big Momma', next to a diver for scale. Note that a large tumor-like growth is visible on the side of the colony (which the diver is inspecting), indicating that methuselahs like this coral may show cancerous signs of their age.
Not only is this coral almost certainly older than Ming the Clam, but it is also still alive (unlike Ming). If we can protect this coral, and others like it, from the combined effects of climate change, overfishing, nutrient pollution and disease - stressors which, combined, ravage reefs worldwide - there is every reason to expect it might continue living for centuries to come.
Although colonial invertebrates like this coral might not fit the standard idea of (solitary) 'animals', they nevertheless qualify for the longevity title, particularly considering the fact that all of the coral's polyps are genetically identical to one another (minus some somatic mutations along the way). Indeed, there is every reason to expect that this enormous coral is the same genetic individual that first settled as a planktonic larva on this distant reef over a thousand years ago."