Fish have memories, thoughts, fears, joys, and dilemmas, and they form an intimate understanding of the world around them. They're intelligent. If they weren't, evolution would've sorted them out of the equation long ago.
A defining need of evolution and an organism to function at all, is the ability to interpret information, act on that information, and in the process store it. The more complicated the environment of an organism is, more it has to be able to remember. Then species social structures can complicate things quite a bit. Obviously they're not as smart as humans (or smart in the same way), but I'd wager that there are plenty of fish that are comparable to dogs and cats in intelligence. It's just very hard for us to recognize intelligence in fish, as they're so far removed from us, from a philosophical standpoint.
Another indication that fish are reasonably intelligent, is the fact that they have a spine, which means that they're Vertebrates, one of the smallest groups of organisms of life. It contains such species as amphibians, reptiles and birds, and also Mammals, which all share common features and plans in their biological make up, one of which is intelligence. This is where we come in. From an evolutionary standpoint, Humans, and most other beings we know for a fact to be intelligent, are actually closely related to Fish, relatively speaking, and so it stands to reason that at least some species of Fish must be considerably intelligent.
Take also the fact that many of the fish we personally keep seem to have different personalities.
There is also plenty of evidence of considerable intelligence outside of the vertebrate class. Take the Octopus for example, a mollusk. Some crustaceans are also known to inhibit signs of intelligence, like the mantis shrimp, and lobsters.