Alaska is part of the United States of America and therefore uses the U.S. dollar as currency. Some stores along the Alaska-Canadian border may also accept Canadian dollars. Traveler's checks should be purchased in U.S. dollars, as traveler's checks from other currencies are not accepted.
Alaskan cruise ships accept U.S. currency and process credit cards in U.S. dollars. Credit cards often have foreign transaction fees, so purchasing traveler's checks can save money. If travelling in both Canada and Alaska, having currency in both forms of dollars reduces the chance of being ripped off when attempting to exchange currency. Always exchange currency at reputable banking institutions.