For humans, eyelids are crucial for keeping our eyeballs clean and moist on dry land, but many animals have different solutions.
In the water, eyelids are not always necessary. Fish eyes are constantly being moistened by their environment, so they do not need eyelids, and although aquatic mammals like dolphins and whales can blink, they do it much less often than we do. Interestingly, it has been argued that as humans evolved from fish, and fish eyes work best when wet, we never lost the requirement for our eyes to be moist.
Back on land different animals have even more creative solutions. In snakes, each eye is covered with a thin, transparent scale, connected directly to the rest of the skin. These scales are fixed into position, keeping the eyes safe at all times but preventing any blinking. Some geckos are also unable to blink, and instead use their tongues to keep their eyes clear of dust and debris.
You may have noticed that cats have a third eyelid called the palpebra tertia. It turns out that quite a few other mammals have this extra membrane and it seems humans may be the odd one out. This contraption is large enough to cover the whole eye, and almost acts like a car’s windscreen wipers. Although the exact use of the third eyelids are not known.
Insects have compound eyes that are completely different to our own, and do not need to be kept wet to function properly, so they have no need for eyelids at all. There is no liquid inside an insect’s eye, and the outside is much like an exoskeleton, hard and protected against the elements (and also against any dust or sand that could damage them). Some have bristles, resembling eyelashes, but these play more of a sensory role, and the same bristles are found all over the body.