There are four main ones
Thixotropic
Viscosity decreases with stress over time. E.g. Some honey (keep stirring and solid honey becomes liquid)
Rheopectic
Viscosity increases with stress over time. E.g. Cream (the longer you whip it the thicker it gets)
Shear thinning
Viscosity decreases with increased stress. E.g. Ketchup (you have to shake the bottle to get it out)
Dilatant or shear thickening
Viscosity increases with increased stress. E.g. Oobleck (cornstarch and water, looks like a liquid but hit it and it is a solid)