What is the record length of time for single-occupant flight?
What is the longest flight time for a single pilot alone in an aircraft?


13 days if a balloon counts as an aircraft.

Balloon

Steve Fossett set a record in 2002


  In 2002, he became the first person to fly around the world alone, nonstop in any kind of aircraft. He launched the 10-story high balloon Spirit of Freedom from Northam, Western Australia on June 19, 2002 and returned to Australia on July 3, 2002, subsequently landing in Queensland. Duration and distance of this solo balloon flight was 13 days, 8 hours, 33 minutes (14 days 19 hours 50 minutes to landing), 20,626.48 statute miles (33,195.10 km).




Other types of aircraft

The following information was volunteered in comments by Scary Spice and Peter Kämpf.

Glider

Charles Atger, stayed aloft for 56.25 hours, solo. 

Powered airplane

Charles Lindbergh was all by himself for 33.5 hours.

Spacecraft

Ron Evans, Apollo 17 Command Module Pilot, was alone for 79 hours, 49 minutes.