At low temperature insulators shows zero resistance..
Research examined the detailed structures and electrical properties of a series of different samples of this material, discovered one important fact; even the part of the molecules not involved in the conduction pathways could qualitatively have an effect on the (super)conducting properties. Only the samples containing the required molecular structures exhibited
According to BCS theory, there should exist electron-phonon coupling in order to have a superconductor. Now in the case of metals, the electron-phonon coupling is very less hence most of them do not superconduct as compared to insulators.
I have attached a formula for the Tc, which depends upon the electron-phonon coupling (V in the formula) and this formula comes from the BCS theory of superconductivity which I took from wikipedia.
I agree with Naiem Ahmed that the structure of special insulators at low temperature is the main reason for the appearance of zero-resistance. We know that the most of solids shrink when the temperature decreases. Some insulators may shrink in such a way that they could be able to form special cavities or paths inside them. So, any free electrons in empty paths could move along them without resistance if, for some reasons, they cannot at low temperature transfer their energy to the walls of channels.
Read for example about the "topological insulators" in quantum Hall effect where the electrons can move along the boundaries of sample without scattering and energy loss.