The short answer is that most have no eye lids. For most fish they just don’t need an eyelid, an eyelid is partially to protect the eye but mostly it helps to stop the eye from drying out. If you think about how the first life evolved in the sea and probably the first eye too so it was only when life moved onto land that an eyelid was needed to stop the eyes drying out. The reason behind blinking is largely to keep the eye clean and since fish eyes constantly have water washing over them they are basically cleaned all the time.
There are actually some fish that do have eyelids, some deep sea fish have what is called an adipose eyelid which is a clear covering over the eyes but they cant blink with it, we actually think it somehow makes there vision better in the deep.
Sharks also have eyelids (and don’t forget they are fish) you can sometimes see this on TV when you see a shark bit into something, they dont blink though and the eyelid is to stop bits of food going into their eyes (sharks are messy eaters 🙂 ) .
Keith has this one pretty much wrapped up. Scientists are unsure why some fish have this adipose tissue over their eyes, some suggestions include
– to protect the eye from debris in the ocean
– acts as a lens to improve vision and focusing
– block out ultra violet light that could damage the eye