LanChile and Aerolineas Argentinas currently have flights that are considered TRANSPOLAR routes between South America and New Zealand (South Pole). These flights reach a very close proximity (in navigational degrees) to the Antarctic continent during the flight.
At ATA, Mark Barnard, L-1011 Fleet Manager, and Gene Freeman, L-1011 Flight Standards Captain, won authority from the FAA to us L-1011s on polar routes. The company envisions using these routes for military contract flying and charter customers in cities such as Seattle.
There is a better article out there about the first polar flight that I'll try to find again.
Last year, I flew on NW from DTW to PEK and back. The westbound flight took the polar route (so it was really northbound!) and the return flight took a more southerly route along the coast of China, Russia, over the Bering Sea, Alaska and Canada.