Although (most of) the replies in this string deal with the matter of airframe efficiency, they have all ignored the matter of engine efficiency.
Greatest range occurs at the speed and altitude giving most miles per hour per pound of thrust, and lowest fuel consumption per hour per pound of thrust. For the airframe this means flying at about 1.35 VMD at the altitude at which the ratio of TAS : Drag is greatest. For jet engines it means operating at between about 85% and 95% RPM.
At low altitudes this RPM range produces too much thrust to fly at 1.35 VMD, so the aircraft must climb. Optimum range occurs at the altitude where the drag at 1.35 VMD is equal to the thrust at between 85% and 95 RPM.
The above applies only in still air, but can be adapted to headwinds or tailwinds by using the speed giving the best Ground speed : Drag ratio rather TAS : Drag ratio.
Fly any faster, slower, higher or lower and range will decrease.
Unless of course the atmospheric conditions are very unusual. To fly half way around the world in a 600 Kt headwind for example you would be better to turn through 180 degrees (asuming this were possible) and fly very slowly!