The answer is entirely dependent on the species of fish. As a general rule, the larger the fish, the more likely they are to sleep. Goldfish and their large coy carp cousins do not sleep. The science behind this is the make up of their brain which lacks a sleep trigger mechanism. Why they evolved (or were intelligently designed) without this function in not entirely clear however there are a few theories. The one which makes the most sense to me is known as the Piscean Intelligence Slave Solution. Within smaller species of fish who are more likely to school, one their member is designated the "brain" of the school. In essence, all other fish in that school are an extension of the brain fish. Whatever the brain fish is thinking or whatever action they are taking, all other fish have an overwhelming compulsion to follow suit. That being the case, it would be a disaster if the brain fish were to sleep as it would render the entire school defenceless. An interesting experiment that supported the Piscean Intelligence Slave Solution was performed in a laboratory at Sea World in Napier, New Zealand. A brain fish was physically isolated from its school by means of putting it inside a clear plastic bag of water. A small hoop was positioned above the tank holding the school, was doused in petroleum and then set on fire. The brain fish was then lifted and passed through the hoop. To the amazement of the scientists conducting the experiment, within a matter of seconds the entire school started making its way to the hoop and began jumping through it without any regard or indeed awareness of their own safety.