What is the furthest anyone has ever been from every other living person? XKCD's Randal Munroe thinks the most likely candidates are the Apollo command module pilots, who were about 2,227 miles from the nearest humans (i.e. astronauts on the lunar surface) during the Apollo moon landings.
That may be the obvious answer, but as Munroe points out in the latest installment of his "what if?" series, there are a number of other contenders who come pretty close.