Fish seem to exhibit a wide range of intelligence.
Octopods, for example, are EXTREMELY intelligent. Usually their intelligence is associate donly with their ability to escape but actually, they are quite capable of problem solving. I watch a show on PBS I think, which demonstrated a series of experiments:
An octopus was given a crab, which it ate.
The same octopus was given a glass jar without lid, with a crab inside. It failed to negotiate it's way in the open mouth of the jar, and was ismply fascinated by the crab through the glass walls.
This same octopus was then allowed to watch the crab being put inside the jar (outside of the tank). The jar was then reinserted, wherein the octopus immediately reached in nd ate the crab.
Now, the jar was sealed, again with a crab inside. The jar was placd in the tanks, and th octopus attacked the top of the jar like it had before when the jar was un-lidded. It failed to retrieve the crab.
Finally, the octopus was allowed to watch the lid be screwed onto the jar, with emphasis on the turning motion it took to do so. When placed back into the tank, the octopus managed to unscrew the lib, and remove the crab.
This intelligence is unlike anything observed in dolphins or birds. A lot of what humans percieve as intelligence has more to do with interspecies communication than actual mental agility. For exmaple, bird "people" will identify the African Grey as the smartest bird, and contest it to be one of the smartest animals. These birds are capable of learning how to identify shapes, and speak their names.
Now, don't we all think that an octopus that can learn to use lids ( a task too complicated for my mother ) could be reasonably assumed to be able to recognize shapes ( it must, of course, in order to be able to recognize a jar with a lid on it ). And yet, how would we know? The bird can tell use that it's performing these simple tasks, however the octopus cannot. One thing is for ceratin though, that a bird cannot be tought complex processes like unscrewing with months of repetition.
Again, consider dolphins, and dogs. They come when called, ******* emotion in via facial expression and tone of voice, and can be tought simple tricks. This convection of thought is usually percieved as intelligence. These animals are by no means dumb, however their intelligence might be over analyzed.
Fish respond to their "name" as well as dogs do, however we can't speak under water so the extent of my experience is fish that come out of hiding when the glass is tapped. There's really no other way to see if fish can respond to verbal commands, save for the experiment that was spoken before about a tirgger ringing a bell if it wanted food.
Where fish seem to lose credence in proving their intelligence is the inability to display emotion or vocalize. Since fish are unable to broadcast these higher level brian activities, the assumption is that they do not have them. However, no argument can really be made to that effect. It's well known that while most fish cannot vocalise or make facial expressions, they can in fact communicate with other sea life in way which are completely indetectable to our own senses. Chemical communication is a widely used form of inter and intra species communication among marine animals. In fact, it really is a more efficient form than vocalization is, since the language of the body is chemical in nature. Skeptics to this theory must conceed that these communications are widely seen and proven in the course of mating. Pheromones released into the water and analogous to saying "I'm a horny fish." We really can't know what might or might not be said in the waters because they don't do so in a way that we can understand.
Finally the debate about ability to learn tircks is moot. Nearly any animal, excluding reptiles, can learn actions through repetition, especially if and insticual condition (food) is involved. It seems that in the case of the octopus, however, it can learn without continual repetition, and even extrapolate information from multiple experiences (i.e. attacking lidded jar from the top, since that's how it got in the unlidded jar). Furthermore, bell ringing triggers demonstrate an ability to deviate form ingrained instinctual behavior i.e. "if hungry, ring bell", rather than "if hungry, look for clams".
Given that fish are certainly cpable of learning through repetition as well as through experience and extrapolation, we can place them higher than reptiles and rodents in intelligence, and in this catagory, on par with dogs, birds, and dolphins. In the case of communication, not much information is gained, but only due to our own lack of understanding. In way's we do understand (glass tapping, and bell ringing) they appear at least as able as dogs, birds, and dolphins, and still brighter than reptiles. I suppose it's quite visible now why it's so hard to speculate on the intelligence of fish, especially since "fish" is such a broad term.
Bottom line, I predict that "fish" in general are more intelligent than reptiles and rodents, and at least as intelligent as larger mammals and large birds.