Nociceptors are receptors in our skin and throughout our bodies that respond to noxious stimuli. For example, when bodily tissue is damaged or subjected to heat or pressure, nociceptors respond and send messages along nerve fibers to our brains, thereby generating the feeling of pain. Teleost fish (fish that are bony, such as trout) have nociceptors too, and their nociceptors look just like ours when viewed under a microscope. This does not prove that they feel pain, of course. But they behave in response to noxious stimuli very much as we do.
For example, trout have nociceptors in their lips structurally very similar to ours. When they are anaesthetized and their lips injected with bee venom or acetic acid (the main ingredient in vinegar), the trout rub their lips against the sides of the fish tank and the gravel on the bottom (once the anaesthetic wears off), and they also sit there and rock from side to side (a reaction in mammals that signifies that they are feeling or have been feeling acute discomfort). In addition, teleost fish engage in trade-off behavior. This is what we do when we hold on to an extremely hot plate full of food, if we are experiencing deep hunger, even though we are experiencing pain. Likewise, when teleost fish go to get food in an aquarium and are then electrically shocked on their flanks, they subsequently stay away from the region containing the food, but as their hunger increases, they return.
There are many such examples of behavioral similarities in teleost fish and mammals in response to noxious stimuli. This is evidence that they feel pain. The inference at work here is similar effect, so similar cause—unless we have reasons for believing that a different causal chain is operative. The inference goes the other way round too: same cause (reaction on nociceptors), so same effect (the feeling of pain), unless again we have reason to believe that a different causal chain is operative.
Some psychologists and philosophers have argued that neurological differences between mammals and fish provide such a reason. It is commonly held that without activity in the neocortex, the area of the brain on the outside that is full of folds, humans cannot feel pain or any other conscious state. Since fish lack a neocortex, this has led to the thought that they do not feel pain or anything else, notwithstanding the similarities in nociceptors and behavior.
This conclusion is too swift. Children born without a neocortex sometimes survive and sometimes they engage in behavior that is strongly suggestive of their undergoing a range of basic emotional and bodily feelings (Merker 2007). For example, they smile and laugh, and show aversion by fussing, arching of the back and crying. Adults known to the children can get them to engage in play sequences in which the children progress from smiling to giggling to laughing and showing great excitement. For example, some decorticate children can be gotten to track the movements of a puppet with their eyes, to smile and apparently to show pleasure as the puppet is waggled before them.
Furthermore, birds lack a neocortex, but it would seem utterly bizarre to insist that they have no conscious states. Birds produce songs of many kinds, which would seem entirely pointless if other birds could not hear them. Birds are also subject to visual illusions of various kinds, which is hard to understand if nothing appears anyway to them. And they respond to painkillers as we do; they also protect and guard damaged parts of their bodies.
So, a strong case can be made for the view that some fish feel pain. But do they all? Sharks lack nociceptors, as do other elasmobranch fish (fish that do not have a cartilaginous skeleton). So, one reason for supposing that sharks feel pain is removed. They also do not respond as teleost fish typically do to noxious stimuli. For example, hammerhead sharks prey on stingrays. These sharks have been found with as many as 96 stingray barbs embedded in their mouths. Apparently, they do not feel pain from the barbs. There are also reports from whalemen of sharks that they have been split in two continuing to feed. Likewise for sharks that have been disemboweled by other sharks attacking them. Apparently their fatal wounds do not cause them to feel pain.
In these respects, sharks are rather like many insects. Unlike mammals, insects do not show protective behavior with respect to parts of their bodies that have been injured. They do not limp, for example, if they injure their legs, nor do they stop feeding or mating even if their bodies are severely damaged. For example, locusts have been observed to continue to feed while they are being eaten by mantises; tse-tse flies that have been half-dissected do not stop feeding; male mantids that are mating continue to mate even as they are being eaten by their partners.
To be sure, sharks caught on fishing lines struggle to get away as other fish do. But this seems no more than a reflex: the line interferes with their free movement and so they reflexively try to free themselves. The weight of the evidence supports the view that sharks do not feel pain. And not feeling pain, they are not deterred from their predations by bodily damage. They are free to continue to hunt and attack. Perhaps the real root of the idea that sharks are natural killing machines lies here, in the absence of pain.
Merker, B. 2007, "Consciousness without a cerebral cortex: a challenge for neuroscience and medicine," with commentaries, in The Behavioral and Brain Sciences 30: 63-134.