This week, Cheeta, the chimp from the original Tarzan films, reached the splendid age of 75 (though he has a few years to go before reaching the 79 clocked up by his co-star Johnny Weissmuller). Diabetic Cheeta, his fur now speckled with grey, celebrated with sugar-free cake and diet soft drinks at his home in the legendary retirement destination of Palm Springs, California, where he passes his days watching TV, painting and playing the piano.

Cheeta is cited by the Guinness Book of World Records as the world's oldest primate (that should be non-human primate, of course, but perhaps they were confused by his lifestyle). But verifying such titles is a difficult business. Consider the case of Adwaita the tortoise, who once belonged to the British colonial general Clive of India in the 18th century. One Wednesday last month, Adwaita was found dead in his enclosure in Alipore Zoo. His death was not unexpected - his shell had cracked some months before and a wound had developed, and he was, after all, somewhat advanced in life: West Bengal officials said records showed Adwaita was at least 150 years old, but other evidence suggested he was more like 255. It will take carbon-dating of his shell to determine his true age. At 255, Adwaita would beat Harriet the Galápagos tortoise, who was reportedly collected by Charles Darwin, and died aged 175 in 2006, and Tu'i Malila, the radiated tortoise given to the royal family of Tonga by Captain James Cook, and who passed over aged 188 in 1965.

The age of a fish is calculated in much the same way as one works out the age of a tree by counting its rings; most fish have growth rings on their scales known as annuli. This technique was used to estimate the age of Hanako, meaning "flower maid", the world's oldest koi carp, who died in 1977 at the age of 226 years. Goldie, the oldest goldfish, had reached the age of 45 by the time he gasped his last in 2005. He was won at a fair in Budleigh Salterton in 1960, and by the time he died his skin had faded from a yellowy orange to a soft pink.

Alas, Goldie never made it to the Guinness Book of World Records because there was no documentary evidence of his age. This is a common problem. While it is simple to check the age of a pedigree cat, for example, as it will wield a certificate of authenticity, the more common moggie comes with no such paperwork. In 2004, Whiskey, a 33-year-old tabby from Essex, staked his claim as Britain's oldest cat, but his owner was unable to prove the claim conclusively. As for the world title, the Guinness Book of World Records held that Creme Puff, a cat from Austin, Texas, died in 2005 aged 38 years and three days, though there has been much jostling for the crown. Guinness at present records the oldest living cat as Kataleena Lady, a 27-year-old Burmese born on March 11, 1977, in Australia.

The title of oldest parrot is also much disputed. Some favour Charlie, a blue macaw allegedly bought by Winston Churchill two years before the start of the second world war, who now resides at a Surrey garden centre, where he fills the air with anti-Nazi tirades. Charlie's owner, who bought him from a pet shop in 1965, claims that he is 104. Unfortunately, the administrators of Chartwell, Churchill's former country home, state that they have no record of any parrot, while Churchill's daughter, Lady Soames, says her father never owned a macaw (though he did, once, have an African grey parrot named Polly).

In 2004 Matilda, a 14-year-old bantam hen, was named the world oldest hen. The world's oldest dove, Methuselah (perhaps not its name since birth), is 31 years 6 months old. He was born in April 1975 and lives in Harxheim, Germany.

It is naturally harder to tell the age of animals that keep their distance from humans, but a Manx shearwater aged 52 is believed to hold the title of the oldest known wild bird. It was first captured off the coast of Wales and ringed by ornithologists in May 1957, when it was between four and six years old, and recaptured in April 2003. It was estimated to have flown five million miles during its lifetime, the equivalent of circumnavigating the globe 200 times.

Some of the humblest-seeming animals are also the longest-lived, like the ocean quahog, a mollusc with an estimated maximum lifespan of 225 years, and the tardigrade, or water bear. Tardigrades are tiny creatures, about the size of a pencil dot, and look much like caterpillars, with four pairs of legs ending in claws, and five body segments. They live mostly in mosses and lichens, beaches and water sediments, and can be found both high in the Himalayas and 4,000m deep in the sea, and from the polar regions to the equator. They are hardy little critters and, though they are they are 70% water, they are able to enter a "cryptobiotic" state, suspending their metabolism and living in a dehydrated state for years. It is believed that their lifespan can stretch to over a century.

At the other end of the size scale, the oldest known elephant reached the ripe old age of 86. Lin Wang was originally from Myanmar, and was captured in 1943 by the Nationalist army from the Japanese troops, then transported to Taiwan in 1947. When he was captured, Lin Wang was nicknamed "the Beautiful", but in his later years the people of Taiwan knew him affectionately as "Grandpa Lin Wang". As his years increased, he developed arthritis in his left hind leg, and began to lose his appetite. One Wednesday morning in late February 2003, Lin Wang was found collapsed at Taipei's Mucha Zoo. Upon his death, workers at the zoo held a minute's silence in his honour.

· Additional research by Jodie Wright.