Donkey's used to be a mode of transport, but also used by farmers to help with heavy lifting and to transport the farmer's produce to the villages. There are two principal strains: a large dark-coloured type with a pale belly, probably of European origin; and a small grey African type which represents about 20% of the total population, which in 2002 was estimated at 2200–2700.
Sadly, once they are too old to work, these little fellows are either killed or deserted. You will not see as many on the island anymore, and the Cyprus Donkey Sanctuary is a retirement home for rescued, ill, deserted, unwanted donkeys.
For just 20 Euros per year, you can 'Adopt a donkey' and contribute towards it's care, at the sanctuary's website.