Tortoises generally have the longest lifespan of any animal; it's not uncommon for them to live past their 150th birthdays. In fact, there are some cultures, such as the Chinese culture, in which the tortoise has come to symbolize long life.
In situations where the age of a tortoise is unknown, there are usually some clues. The number of concentric rings on the carapace is a good bit of evidence, although it does come with its limitations. For example, if food and water are always readily available, that can limit the appearance of rings. In other circumstances, simple wear and tear can remove any visible traces of rings.
Now let's look at the case of a tortoise named Tu'I Malila. The animal was given as a gift by British explorer Captain Cook to the royal family of Tonga in 1777 shortly after it was born. It died in the relatively recent year of 1965.
If you don't want to do the math yourself, that would make Tu'I Malila 188 years old at the time of it's death. To be sure, this gift outlasted many generations of the royal family.
The picture here is of the preserved remains of Tu'I Malila.