It is important to note the distinction between a thixotropic fluid and a shear thinning fluid:
Some fluids are anti-thixotropic: constant shear stress for a time causes an increase in viscosity or even solidification. Constant shear stress can be applied by shaking or mixing. Fluids which exhibit this property are usually called rheopectic. They are are much less common.
Drilling muds used in geotechnical applications can be thixotropic. Honey from honey bees may also exhibit this property under certain conditions.
Some clay deposits found in the process of exploring caves exhibit thixotropism: an initially solid-seeming mudbank will turn soupy and yield up moisture when dug into or otherwise disturbed. These clays were deposited in the past by low-velocity streams which tend to deposit fine-grained sediment.
Examples of applications for thixotropic fluids are the thickening of food stuffs and medical products. Toothpaste is thixotropic, which allows it to be squeezed out of the tube, yet retain a solid shape on the brush. The ink developed for the Fisher space pen is thixotropic so that the ink flows only when the roller ball is pressed on paper. Ketchup is frequently thixotropic.
Modern alkyd and latex paint varieties are often thixotropic and will not run off the painter's brush, but will still spread easily and evenly, since the gel-like paint "liquefies" when brushed out. Many clutch-type automatic transmissions use fluids with thixotropic properties, to engage the different clutch plates inside the transmission housing at specific pressures, which then changes the gearset.
Many kinds of inks--used in silkscreen textile printing--made from plastisol, exhibit thixotropic qualities. Some--such as those used in CMYK-type process printing--are designed to quickly regain viscosity once they are applied to protect the structure of the dots for accurate color reproduction. This is a sort of reverse thixotropy.