Rabbits blink, but not often, because they have a third eyelid. The third eyelid allows rabbits to sleep with their eyes open. The rabbit's third eyelid is called the nictitating membrane.
The nictitating membrane floats across the surface of the rabbit's eye to lubricate and protect the cornea. Humans blink to lubricate and protect the surface of the eye. Besides rabbits, dogs, cats and other mammals have a third eyelid. Many reptiles, birds and sharks have a third eyelid. Camels are the largest mammals with a nictitating membrane. The third eyelid keeps sand, water, wind and other elements out of the animals' eyes.