Perhaps a bit of overview is in order here. Reynolds Number belongs to a class of dimensionless numbers of Fluid Mechanics. These unitless numbers are used for studying and comparing physical phenomenons at various scale factors. They are useful because one can build a scale model, which despite being physically smaller has similar dimensionless numbers as the full size counterpart.

An example is that one can study the aerodynamics of a scale model aircraft and relate it to the full size airplane by adjusting the parameters to achieve the same Renolds Number, Re, as the full size plane. Since:

Re = Length x Velocity / Viscocity

if we have a 1/8 scale model in a wind tunnel, we can crank up the airspeed to 8 times the normal flight regime of the full-scale aircraft and achieve the same Reynolds Number. Then the tests will fairly accurately predict full scale results.

Likewise, we can keep the airspeed the same and use fluid that has 1/8th the viscocity, and the resultant Reynolds Number will still be the same.

I remember when I took my Fluid Mechanics class, Reynolds number was the big one, since it's applicable to constrained (pipe) and general fluid flow. Others D-less numbers mentioned as commonly used are Weber's Number and Rayleigh's Number, which are useful for surface ship design, and Euler number. Drag coefficient, Cd, is also another common D-less number.