The key to being comfortable in all conditions is to wear clothing you can layer as it gets cooler, or remove as temperatures rise.
For most cruises, I leave my blue jeans at home, but in Alaska they serve as staples to wear in ports of call, on excursions, and even onboard for day wear while visiting Glacier Bay, or cruising the Inside Passage.
At times, we've been fortunate enough to experience "shorts weather" in Alaska. So don't assume Alaska will always be cold: Bring along a swimsuit and a pair of shorts. But when we've flown up to, and landed on, glaciers, we were delighted we'd brought along warm socks, gloves, polartec fleece or parkas.
We've found evening dress on the ship during our Alaska cruises to be generally more casual. Formal nights can still be quite formal, but on most ships, all other nights are casual attire. Therefore don't feel compelled to pack sports jackets and ties or extra cocktail dresses.
Even in the Caribbean, backpacks are handy for carrying beach towels, coolers and items you purchase along the way. So it's not something you'll only use in Alaska, if you choose to purchase one before you go.
If you're planning to take some of the many "adventure excursions" available in Alaska, I highly recommend investing in a pair of hiking boots, rather than wearing sneakers. They're comfortable for walking around town, and combined with a good pair of socks, can keep your feet warm and dry in inclement weather.
There are a couple of non-clothing items that are MUSTS for an Alaska cruise. (1) Insect repellent: In some areas you won't be able to tell if it's mosquitoes or 18-wheelers coming at you. (2) Binoculars, for close-up viewing of wildlife and glaciers. (3) More film than you think you'll need. The scenery is truly breathtaking, and you'll be surprised at how many times you click!
A must on my personal packing list is my antlers. But I always check to see if it's hunting season before I book the cruise.