From the FIFA ranking, not from the face of the Earth :)
Their most recent match was a 2 - 1 loss in a friendly against Solomon Islands on 13 July 2007. Since the July 2011 FIFA ranking will be publish on 27 July 2011 (more than 4 years after that match), Papua New Guinea will no longer be listed in the ranking.
Next up: Samoa and American Samoa - will no longer be listed in the September 2011 ranking.
The next two teams are from CONCACAF (US Virgin Islands and Turks and Caicos Islands) set to dissappear from the rankings in March/April 2012. However, I think they will participate in the 2014 World Cup qualifiers and will avoid being dropped from the ranking.
Sao Tome and Principe are unranked since November 2007. Their most recent match was an 8 - 0 loss in a 2006 FIFA World Cup qualifier against Libya on 16 November 2003.