The rarist and most unusual bike I have would probobly be my 1978 Ducati GTL 500 paralell twin that my wife got for me as a Christmas present in 1980 to replace the Harley XLCR 1000 that got stolen the previous July. I'm not sure but I don't think more than 50 made it to the US.
Picture is from last summer at a local Ducati display
Or it could be my 1953 NSU 250 Max
Currantly awaiting restoration.The most unusual feature it has is what NSU called the Ultra max drive for the overhead cam, there is an ecentric on the end of the crankshaft and a matching ecentric on the end of the cam with two connecting rods similar to the drive rods on a steam locomotive to operate the cam, No chincey chains or expensive complicated shafts and bevel gears here! It was an extremely well built and fine running motor.