Almost every fish sometimes stays in a state of energy conservation, which we can call resting or even "sleeping", although this behavior may not be the same as "sleeping" in most land animals.
Many fish (such as perch) sleep on or under logs at night. Coral polyps are active during the day and rest in the cracks of the reef at night.
Fishes look very different when they are resting than at other times. For example, many small carps that gather together and are very active during the day disperse at night and remain motionless in shallow water. Some fish rest during the day and are active at night, but almost all fish sleep.
Some animals swim non-stop because they have to keep spitting out water to keep breathing; but they may still sleep while moving, we just don't know it.
