Who is the most famous granny in the world?

That has to be Maria Ann Smith. To those who knew her, they called her "Granny Smith". 

To those of us who don't know her personally, we are acquainted to her by the green apples that we partake as they are or in processed forms such as apple pie and apple strudel.

Here then is an extract from Wikipedia for a bite of history on the Granny Smith from Australia that is now renown all over the world:-

The Granny Smith Cultivar originated in Eastwood, New South Wales, Australia (now a suburb of Sydney) in 1868. Its discoverer, Maria Ann Smith, had emigrated to the district from Beckley, East Sussex in 1839 with her husband Thomas. They purchased a small orchard in the area in 1855-1856 and began cultivating fruit, for which the area was a well known centre in colonial Australia. Smith had eight children and was a prominent figure in the district, earning the nickname "Granny" Smith in her advanced years.

The first description of the origin of the Granny Smith apple was not published until 1924. In that year, Farmer and Settler published the account of a local historian who had interviewed two men who had known Smith. One of those interviewed recalled that, in 1868, he (then twelve years old) and his father had been invited to Smith's farm to inspect a chance seedling that had sprung near a creek. Smith had dumped there, among the ferns, the remains of French crab-apples that had been grown in Tasmania. Another story recounted that Smith had been testing French crab-apples for cooking, and, throwing the apple cores out her window as she worked, had found that the new cultivar had sprung up underneath her kitchen windowsill. 

Whatever the case, Smith took it upon herself to propagate the new cultivar on her property, finding the apples good for cooking and for general consumption.Having "all the appearances of a cooking apple," they were not tart but instead were "sweet and crisp to eat." She took a stall at Sydney's George Street market, where the apples stored "exceptionally well and became popular" and "once a week sold her produce there."

Now, we can add green apples as another icon to associate with Australia all thanks to Granny Smith.