For those who are using the NGS Online Inverse Geodesic Calculator:
http://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/inverse2.prl
be careful. Especially between two near-antipodal locations, the computed distance shows an error of some tens of kilometres !!! The origin of the numeric trouble was identified long time ago by Thaddeus Vincenty (page 92):
http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
In any case, it is preferrable to use the reliable and very accurate online calculator by Charles Karney:
http://geographiclib.sourceforge.net/cgi-bin/Geod