neutron energy...  comparable to energy of atomic and molecular motions & high resolution microscopic dynamic analysis 

neutron wavelength...  comparable to interatomic distances & structure analysis from atomic to macromolecular scale

neutrons see nuclei...  light atoms are visible in the presence of heavy ones 

neutrons have a magnetic moment...  easy study of microscopic magnetic structure and dynamics

neutrons are neutral (highly penetrating)...  microscopic properties of bulk samples observable; radiography on finished industrial products  (e.g. engine blades) possible

neutrons are non-destructive...  even to complex, delicate biological samples

Links - Information in other Websites

In English: Nanopolis - Neutron Applications - Fundamental Research - Introduction
In German: Weshalb Neutronen so begehrt sind (PSI-SINQ)