WASHINGTON, D.C.—Odysseus, who voyaged across the wine-dark seas of the Mediterranean in Homer’s epic, may have had some astonishingly ancient forerunners. A decade ago, when excavators claimed to have found stone tools on the Greek island of Crete dating back at least 130,000 years, other archaeologists were stunned—and skeptical. But since then, at that site and others, researchers have quietly built up a convincing case for Stone Age seafarers—and for the even more remarkable possibility that they were Neandertals, the extinct cousins of modern humans. The finds strongly suggest that the urge to go to sea, and the cognitive and...