My fish definately sleep. My cichlids, angelfish, gouramis are totally out of it in the morning if I wake up earlier than usual. They sleep with their eyes open obviously and don't really notice where they are swimming or just hover that the same spot. If I wake up earlier than usual and feed them right as I turn on the light, most of them are sleeping and won't even notice I've fed them.
My puffer fish sleeps too. He sleeps under the bogwood at night and comes out during the day.