Antarctica
In the southern hemisphere, most intercity pairs do not result in a great circle route over Antarctica. Although direct flights between South Africa and New Zealand would overfly Antarctica, there never have been direct flights between those countries.
Aerolineas Argentinas operate nonstop services between Sydney and Buenos Aires, LAN Chile operate nonstop services between New Zealand and Santiago and Qantas operate nonstop between Sydney and Santiago, forming the most southerly polar route. Depending on flight-level winds, these can approach 55 degrees southerly latitude, though not enough to cross the polar ice cap.
Read more about this topic: Polar Route