Even an ordinary metallic conductor isn't well-described by the classical picture of electrons colliding with nuclei. Because the electrons are wave-like objects, they actually transmit through a regular crystalline array of nuclei without scattering, much as a light-wave transmits through a diamond. The scattering that causes the resistance comes from the thermal jiggling of the atoms and from the occasional irregularities in the crystal, from defects and impurities. Typical metals get less resistive as they cool because the thermal jiggling is reduced.
In a superconductor, the electrons themselves fall into a collective state. In order for an electron to scatter, it has to jump out of that state into one of higher energy. As the temperature is lowered, such jumps become extremely rare, and the resistivity rapidly approaches zero.
For a given current, I, as R gets close to zero, V then also gets close to zero. In many common superconducting devices R gets so small that V is too small to measure even when there's some usefully large I.
(published on 08/21/2010)