Jacket
Unless you plan on spending time in the snowy mountains, a heavy winter jacket isn't necessary. A windbreaker or light jacket with a lining will work well for sea and shore activities. Even better would be a water-resistant jacket so you're prepared for rain.
Sweater and/or Sweatshirt
These two items are good for layering. A short-sleeve shirt and shorts or slacks might be all you need during the day. Then throw on a sweater or sweatshirt when the weather starts to cool down.
Pants
Bring a pair of shorts, but long pants such as jeans and khakis will serve you well. Add to that a pair of dress slacks for more formal activities.
Formal Attire
Alaskan cruises tend to be fairly casual, but most cruise lines still have a formal dinner party. That would most likely mean a dark suit for men and a cocktail dress for women.
Shoes
When you're exploring, not many things can spoil a vacation more than blisters. So bring comfortable walking shoes with rubber soles. If you anticipate checking out more treacherous terrain, a pair of hiking boots will serve you well too.
Miscellaneous Items
They don't take up a whole lot of space, so it might not be a bad idea to throw in a pair of light gloves and a hat or visor. Sunglasses also are recommended.