Back in the 1930s, design was totally unrestricted. You want a streamlined motorcycle? No problem. You want the engine mounted in the front wheel? No problem. You want spiral exhausts? No problem. You want all that in one package? With the Killinger und Freund Motorrad, it was no problem at all.
The Killinger and Freund, like all great designs, was pretty much the answer to a question no one had asked. It began as an attempt at improving upon the front-engined Megola motorcycle, with its clutch-less and transmission-less front-mounted engine. And a front-mounted engine meant that the bike was essentially backwards, as virtually all modern motorcycles send their power out the back.
That was all very well and good, I suppose, but besides the red paint, the Megola isn't very pretty. The Killinger und Freund aimed to rectify that. Coupled with the fact that it was 1935, and aerodynamic design had advanced to the point where people knew what looked good, but didn't know enough to know what actually worked well, the Killinger and Freund was essentially a beautifully unrestricted piece of pure style.
The first order of business was to get a new engine. A lighter, three-cylinder air-cooled engine was installed, this time with a clutch and a two-speed transmission. Again, everything was packaged into the front wheel, which made replacing most of the moving parts a snap. Literally.
You just took off the front wheel.
Everything looked good as well, with both tires in protective covers, which also had the effect of keeping out mud and dirt.
Like so many pre-World War II designs, the Killinger and Freund never made it to mass production, with only a few prototypes at most being built. After the war, American GIs found a lone prototype near Munich, and subsequently posed with a bunch of pictures with it, because that's exactly what you do when you find such a gorgeous piece of machinery lying in the smoldering ruins of post-war Europe.
We don't know for certain its whereabouts, but we do know that holy crap it looks good.
UPDATE: It looks like the motorcycle has been found, or at least the major parts of it have been found. The story that it may have gone back to Germany might have been a fabrication, though its exact current whereabouts seem to have been left intentionally murky. You can see pictures of its current condition here. H/t to Andy88!