As a small kid, I was told that fish don't feel any pain when they bite into a fishing hook. I'm not sure if this was just something made up so I didn't feel sorry for the fishies.
It appears that the controversy is quite widespread.
Slate even had a piece on it:
There is a new study out that contends fish feel pain. A professor at Purdue and his Norwegian graduate student attached small foil heaters to goldfish. Half of the goldfish were injected with morphine, half with saline, and then the researchers turned on the attached micro-toasters. After the heat was gone, the fish without painkillers "acted with defensive behaviors, indicating wariness, or fear and anxiety." They had also developed a lovely brown crust. These results echo a 2003 study by researchers from the University of Edinburgh who shot bee venom into the lips of trout. The bee-stung fish rubbed their lips in the gravel of their tank and generally seemed pissed off.
The 2003 Edinburgh study confirmed that trout have polymodal nociceptors around their face and head—i.e., they have the ability to detect painful stimuli with their nervous system. But, according to some definitions of pain, the detection of painful stimuli is not enough. The animal must have the ability to understand it is in pain to really feel pain.
WFN(World Fishing Network) has an article that contradicts the findings on Slate:
Do fish feel pain when we hook them? Well, not according to Dr. James D. Rose.
[...] “Fish have the simplest types of brains of any vertebrates,” he says, “while humans, have the most complex brains of any species. Conscious awareness of sensations, emotions and pain in humans depends on our massively developed neocortex and other specialized brain regions in the cerebral hemispheres. If the cerebral hemispheres of a human are destroyed, a comatose, vegetative state results. Fish, in contrast, have very small cerebral hemispheres that lack neocortex. If the cerebral hemispheres of a fish are destroyed, the fish’s behavior is quite normal, because the simple behaviors of which a fish is capable (including all of its reactions to nociceptive stimuli) depend mainly on the brainstem and spinal cord.”