Aparrently cats and dogs for a start.
The nictitating membrane (from Latin nictare, to blink) is a transparent or translucent third eyelid present in some animals that can be drawn across the eye for protection and to moisten it while maintaining visibility. Some reptiles, birds, and sharks have full nictitating membranes; in many mammals, a small, vestigial portion of the membrane remains in the corner of the eye. Some mammals, such as camels, polar bears, seals and aardvarks, have full nictitating membranes.
The nictitating membrane in cats and dogs does not have many muscle fibers, so consequently is not usually visible, and its being chronically visible should be taken as a sign of poor condition or ill health. It can, however, be seen clearly when gently opening the eye of the healthy animal when it is asleep, or pushing down/applying pressure on the eyeball will cause it to appear. In some breeds of dogs, the nictitating membrane can be prone to prolapse, resulting in a condition called cherry eye.