Newtons law of viscosity is not a fundamental law of nature, but rather a constitutive equation (like Hookes law, Ficks law, and Ohms law) which serves to define the viscosity . Its form is motivated by experiments which show that for a wide range of fluids,  is independent of strain rate. Such fluids are called Newtonian. Gases, water, and many common liquids can be considered Newtonian in ordinary conditions and contexts. However, there are many non-Newtonian fluids that significantly deviate from this behavior. For example:
* Shear-thickening (dilatant) liquids, whose viscosity increases with the rate of shear strain.
* Shear-thinning liquids, whose viscosity decreases with the rate of shear strain.
* Thixotropic liquids, that become less viscous over time when shaken, agitated, or otherwise stressed.
* Rheopectic liquids, that become more viscous over time when shaken, agitated, or otherwise stressed.
* Bingham plastics that behave as a solid at low stresses but flow as a viscous fluid at high stresses.
Trouton's ratio is the ratio of extensional viscosity to shear viscosity. For a Newtonian fluid, the Trouton ratio is 3. Shear-thinning liquids are very commonly, but misleadingly, described as thixotropic.
Viscosity may also depend on the fluids physical state (temperature and pressure) and other, external', factors. For gases and other compressible fluids, it depends on temperature and varies very slowly with pressure. The viscosity of some fluids may depend on other factors. A magnetorheological fluid, for example, becomes thicker when subjected to a magnetic field, possibly to the point of behaving like a solid.