The Viking Longship is easily one of the best harassment units in the game. Its battle statistics are superior in every way to the Galley it replaces, but that's far from its only quality. Thanks to it, any civilization with coastal cities is in grave danger - if Harald decides to attack, no tile next to the Coast is safe, and neither is any civilian located on such tiles.
The best strategy for using Viking Longships is to survey and locate any civilizations with coastal cities as quickly as possible, then declare a Surprise War on them and invade with Longships. Before the enemy knows what hit them, the Norwegians will have pillaged everything...and, without actually taking any territory, amassed some nice plunder to boost their early development!
'A furore Normannorum libera nos, Domine.' The famous prayer, usually uttered by hapless folk upon first sight of the sails of the Vikings’ longships, sums it up. From Ireland to the walls of Paris, the longships carried the fierce Norsemen to kill and plunder. But they also carried Norse explorers across the North Atlantic to Iceland, Greenland, and North America. And traders as far as Rome and Constantinople. Indeed, the longships were the apex of European naval design from the 9th through 13th centuries. Viking longships came in various types; by far the most infamous is the drekkar, a graceful, narrow, shallow-draft vessel, ornately decorated (dragons and snakes and the like), used primarily by those who went raiding. Not only were the drekkar able to sail deep waters, but their shallow draft meant these could navigate up rivers … useful in pillaging cities like Paris.