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 The Alaska cruise season runs from May to September, with high season typically June through August. However, the best time to go is rather subjective.

June, July and August are the warmest months (highs: 50's - 70's), but they also can be quite rainy. The further into the summer you are, the better your chances of seeing wildlife on the various expeditions; these months are the best bets if you want to go fishing as a shore excursion.

May and September offer cheaper cruise fares and fewer crowds; however, shore excursions have a greater chance of being canceled than they do in high season -- especially boat and helicopter tours. May is one of the driest months in the Inside Passage region, but you may find snow on the ground -- great for scenic photos, less ideal for hiking. September offers the best possibility for catching the Northern Lights, as well as great end-of-season shopping deals for souvenir-hunters. However, at this time, the Gulf of Alaska is the choppiest and not recommended for travelers who get seasick. Also, Denali National Park has been known to close in September due to snow.

http://www.cruisecritic.co.uk/articles.cfm?id=1353