Is a superconductor really a super conductor? It is known that a superconductor is a material with electrical resistance zero. My question is, it is exactly zero, a theoretical zero, or for practical realistic reasons it is effectively zero?
 A: Below certain critical thresholds, such as temperature, current, magnetic field and magnetic impurities, the DC resistance is exactly zero.
A: Physics theory and experimental reality have something like a mathematical  epsilon delta relationship, imo.
Here is a review of the matter. From the introduction  in the PDF of the paper Resistance in Superconductors:

The ability of a wire to carry an electrical current with no apparent dissipation is doubtless the most dramatic property of the superconducting state. Under favorable conditions, the electrical resistance of a superconducting wire can be very low indeed. Mathematical models predict lifetimes that far exceed the age of the universe for sufficiently thick wires under appropriate conditions.
In one experiment,a superconducting ring was observed to carry a persistent current for more than ayear without measurable decay, with an upper bound for the decay rate of a part in 10^5 in the course of a year. 
However, in other circumstances, as for sufficiently
  thin wires or films, or in the presence of penetrating strong magnetic fields, non-zero  resistances are observed.

Some experimental plots are included.
A: Yes and no. When you get down to certain geometric extremes (1D, 2D), you start to have other effects that result in non-zero resistance (phase slips, vortices).
You can effectively think of a bulk superconductor in 0 magnetic field while also below the critical current and temperature as having zero resistance.
A: The resistance of a supercurrent is exactly zero. Supercurrents have a universal cause — the Bose-Einstein-Condensation (BEC) of electron pairs as bosons, because BEC-bosons have a minimum and quantized kinetic energy and, thus, cannot transfer their energy to other particles by arbitrarily small portions. Therefore the supercurrent can flow forever.
