Obviously the expected answer is the summer but we went in September, the last cruise of that season, and although we had some rain we were very lucky with the weather and in Ketchikan which gets 13 feet of rain a year we had a brilliant and dry time. It was also, they told us one of the best whale watching trips out of Skagway that year. The beauty of it was that it was also one of the cheapest of the Alaska cruises. So pick and pray really but it's a great cruising area...Nei.
We went to Alaska 24th August this year from Vancouver, we too had lovely weather, except for Ketchigan where we had a very wet day. Hubbard Glacier was viewed in brillant sunshine and was unforgetable. Choose your date and hope for the best I think because I'm sure you'll love it.
We went in mid-May last year & the weather was fantastic. No rain, blue skies, perfect. We chose a repositioning cruise, from LA on Celebrity Summit which had the added bonus of being a longer cruise than just 'Alaska'.