Why are the German professors addressed as Prof. Dr. XXX? I notice that in Germany, basically all the professors are addressed as Prof. Dr. XXX, say Prof. Dr. Mueller. 

However, in other parts of the world, only Prof. would be sufficient,  since a non-doctor can never be a University professor. 

So why are the German professors addressed this way? Isn't it kind of redundant?
In Germany, in rare cases also non-doctors can become a professor. Then it's just "Prof. Müller". Regarding Doctors, we don't have a "PhD" title. "Dr." is the official title for a doctor which is traditionally a prefix to the full name.

See also: http://en.wikipedia.org/wiki/Doctor_(title)#Germany