Whales have an interesting trick when sleeping -- they do it with half of their brain still open for business, as DNews reported in this 2011 video recounting a study of whale sleep that included captivating footage of a pod of sperm whales snoozing.
As the DNews video notes, whales nap in fairly brief intervals, because they need to surface for air. Land mammals such as humans breathe involuntarily, but undersea mammals such as whales and dolphins have to consciously choose to breathe. Sleeping with a shut-down brain, of course, would make that choice a difficult one to make. That's where the half-their-brain thing comes into play. A whale may be "sleeping" but it isn't so down for the count -- brain-function-wise -- that it won't be conscious of the need to come up for air.
One look at a humpback whale makes it easy to see why they need their rest. It must be tiring just being a humpback whale. They're enormous creatures that can grow to nearly 60 feet long and weigh a whopping 40 tons.