Packing for a cruise in a northern summer climate like Alaska is obviously different than one in the tropics. On a calm sunny day you can suntan on your ship balcony, but if and when the weather changes or you go on a shore excursion you need to choose attire accordingly.
So here are some tips to think about and keep in mind this is not an exhaustive list. We're assuming you've got a handle on all your personal items like underthings, toiletries, etc.
~Formal attire. Many ships have a handful of dining areas to choose from, but usually at least one which requires reservations, and for men, a suit jacket and dress pants. Ladies will want to bring a favorite dress or three. So depending on how often you plan to dine in the ship's upscale areas, pack more or less dressy.
~Rain gear. The Inside Passage can be wet, so be sure to bring a water-resistant jacket. Try not to economize on this. Find something that's half fashionable with a light waterproof material, because you could end up wearing it for a whole day in one of the ports.
~Sweaters (and warm clothing). As mentioned above, Alaska in the summer is a more challenging packing task than a tropical holiday, so you'll need some warm layers (cardigans, hoodies and fleece sweaters) for chilly evenings on the ship-deck.
~Bathing suit. It's very easy to forget this and you will need it for the ship swimming pool and when the sun comes out.
~Shorts and T-shirts. Ditto for these.
~Hiking/walking clothes. What you pack here will depend on the exertion level of your excursions. For most larger group tours people are quite happy with jeans. For more vigorous ones you'll perhaps want to consider athletic wear.
~Footwear. Again, it's surprising when packing for a cruise (or any vacation for that matter) how little thought gets relegated to footwear. At minimum take one pair of comfortable, durable hiking/walking shoes (preferably water-resistant). And of course for dining in-ship bring something suitable for formal nights; and sandals are helpful for warm days around the ship.
~Sunglasses and a cap.
~Camera gear. You will want to record your Alaska trip, it's sights, scenery and experiences--that is a given. In 2016 the question is how? There are now so many options. Many people, because of the physical space restrictions created by the extra clothing needed for Alaskan cruises, choose to use their phones for photos and video. This is now a viable option since the cameras in phones have improved so much. Just keep in mind the critical issue of image storage space with this option.
It's one of the reasons why I recommend bringing a dedicated camera for this trip, not to mention the capability of taking higher quality images. Different camera options here are point and shoots, bridge cameras and full DSLRs. GoPros are also another category. Do some research. You'll be balancing portability, ease and simplicity, with cost, image quality and carry weight.