Depends on the material of your pillow fill.
For natural feather down:
They should really only be dry cleaned and not machine washed because of two main reasons:
First, the feathers will lose some fluffiness when soaked in water; the more you wash it, the more flat and clumpy the pillow becomes.
Second, the feather fill inside pillows are often treated with antibacterial chemicals, as it IS an animal by-product that could harbour unwanted bacteria. These chemicals are water-soluble, and are not safe for you.