Baobab
This particular baobab is rumoured to be approximately 4000 years old. To put that into context, at the time this tree was a seedling, workmen had just submitted the final invoice for the completion of Stonehenge.
The tree remains leafless for most of the year, giving the impression of having been planted upside down. Even stranger, it does produce flowers - but only at night.
They are very difficult to kill and the smooth bark is loved by elephants, who strip it away in order to get at the water inside. The tree simply grows more bark!
Interestingly, the tree stores water in its trunk and so apparently grows and shrinks throughout the year.