Weight
Reducing weight is the biggest sole factor in determining how long an aircraft can stay airborne. Heavier planes require more lift and thus more air speed, which burns more fuel. Minimizing takeoff weight not only conserves fuel, but allows the engine to operate on a lower throttle setting to maintain proper cruising speed.
Fuel
Maximizing the aircraft's available fuel capacity will extend flight times and overall range. Additional fuel cells can often be fitted to provide extra flight time for long haul trips. Special attention must be paid not to upset the plane's balance or center of gravity. You may also set engine fuel trims slightly leaner on some aircraft to conserve fuel.
Altitude
Air causes resistance, or drag against all the plane's surfaces. This resistive force must be overcome by the engine. Flying at higher altitudes will reduce drag and can extend flight times significantly. However, keep in mind that the thinner air found at these altitudes will reduce engine output and horsepower in piston-powered engines.
Gliders
Gliders are not powered in the conventional sense, but rather rely on thermals, or strong updrafts of air, to stay in the air. Finding the perfect coastal area or mountain pass (and the perfect day) is crucial for achieving the longest duration flight. A craft with a high glide ratio will stay aloft for a longest time. The glide ratio refers to the distance a plane can cover as a function of altitude. For example a 20 to 1 ratio indicates the plane can travel 20 miles for every mile of altitude it maintains.