The farthest a human being has ever been from Earth was during the Apollo 13 mission, when Americans James Lovell, Fred Haise, John Swigert passed over the far, or "dark" side of the Moon at an altitude of 158 miles (254 km) from the lunar surface. This works out to approximately 400,171 km (248,655 miles) from earth. This record was achieved at 0:21 UTC on April 15, 1970. The record has stood for almost four decades, and seems unlikely to be surpassed before 2020, when both Japan and the United States are scheduled to return to the Moon. For comparison, the distance between New York and Tokyo is 10,878 km (6,760 miles).
The record was achieved when the mission's original objective, to land two men at the Fra Mauro Highlands on the near side of the Moon, was scrubbed due to an oxygen tank explosion. Instead of landing, the craft was sent into a free return trajectory, using the Moon's gravity as a slingshot to return to Earth. Normally this would have been a simple procedure, but a significant course correction was required, and due to the explosion, ground operators didn't want to risk firing the main engine. So, the lunar module's descent engine was used instead.
All the manned Moon missions involved one person of the three-person team staying in lunar orbit while the other two visited the surface. The orbital period was about two hours, and the altitude ranged between about four and a hundred miles. Therefore, at least several people came close to matching the distance from Earth record set by the crew of Apollo 13.
There are no plans for a manned mission to the Moon until 2020, when both the USA and Japan plan to make a visit. The exact specs of these missions are currently unknown, so we don't know for sure whether they'll break the record for furthest person from Earth.
Past 2020, the possibility of a Mars mission is open. If successful, this would shatter the distance record for a human from Earth by a factor of at least 100.