There are people who say that some species do sleep. See for instance http://www.scielo.br/pdf/bjmbr/v32n10/3339m.pdf
They do rest and go into some sort of sleep, especially if it is totally dark, but I agree with Pieter, I would not call it sleep. However, I do believe that some functions go into resting mode.
In nature, fish have predators, and if they completely shut down, they will obviously be prey very soon. Think about some fish in nature who constantly have to fight currents.