The best military bike of World War II was almost certainly Germany's BMW R75. This machine had oil-damped telescopic front forks, rather than the primitive girder suspension of the day. And with shaft drive and superior cooling the flat twin performed exceptionally, especially in the African desert.
The Japanese were obsessed with their knock-off Harleys, while the Italians used a rugged 500cc forward-facing flat single - the Moto Guzzi Alce. So, mysteriously (to me anyway) the Axis powers did not seem keen to share the R75 concept, but their enemies knew a great design when they saw it.
The Russian M72 was a near clone of the R75 and the US Army asked both Harley-Davidson and Indian to see if they could produce a similar shaft-drive motorcycle. In 1942, Harley replicated the BMW engine and transmission, converted metric measurements to inches and produced its version - the 750cc shaft-drive XA.
These BMW R75 knock-offs apparently performed quite well, but Indian developed a better-looking shaft-driven design - a transverse V-twin reminiscent of a post-war Moto Guzzi.
Uncle Sam eventually rejected both bikes, deciding rather to increase use of its more versatile Jeep. Far easier to operated than a bike, one of these could transport not merely two soldiers but if need be a whole squad.
As for the Limeys, though excellent off-road designs were tried out, back in the 1930s the British Army astonished everyone by choosing a bland 500cc road bike - the BSA M20. True, there were worse bikes than the M20, but producing just 13bhp at 4200rpm, some commentators considered them outdated even before they went into mass production. The four-speed M20 certainly was cheap to manufacture, simple to operate and super-reliable. Despite sluggish performance and poor ground clearance more than 126,000 units were built, making the M20 the most widely produced bike of World War II. Motorcycle historian Frank Melling sums it up: "Almost every BSA rider would have dumped their M20 in a ditch at the first opportunity, in order to have the vastly better Matchless G3/L."