Newton's law of viscosity is a constitutive equation that describes how a fluid resists attempts to move through it. It holds true with some liquids and fails in others. Therefore, it is not considered a fundamental law of nature.
A Newtonian fluid has a constant viscosity, which means that it continues to act like a fluid independently of the stress applied to it. When force is increased, there is more resistance. This amount of exertion remains proportionate regardless of the amount of force applied.
Non-Newtonian fluids do not have a constant viscosity. The resistance of the liquid varies depending on the amount of force administered. Oobleck is considered to be a non-Newtonian liquid because it behaves like a solid when enough force is applied.
According to About.com, a liquid with a low viscosity, water for example, is thin. A higher viscosity means that a liquid is thick, like honey. According to Wikipedia, a liquid's viscosity usually depends on its composition and temperature, even if it is a Newtonian liquid.
There are other factors that can affect a liquid's viscosity, such as exposure to a magnetic field. Many non-Newtonian fluids deviate from the law, including shear thinning or thickening liquids, thixotropic liquids, rheopectic liquids and Bingham plastics.