This is probably the most important question you will ask yourself after all arrangements are made. Here are just a few guidelines.
At least one, and possible two nights (on a 7 day cruise) will be designated as "formal". Ladies, this means your finest - ranging from a long black skirt with a glittery top to a cocktail dress. Gents, on our cruise, very few men wore tuxedoes, most wore dark suits. Another night will be designed as "semi-formal" and just about the same attire is appropriate. All other evenings, passengers are expected to dress "smart casual"- something you would wear to a nice restaurant.
During the day, depending on the weather of course, shorts, jeans, slacks comfortable shoes are appropriate both on the ship and for shore tours. No matter the weather - pack a swimsuit; the pools are great and the hot tubs even better. On Princess you will be provided with a nice bathrobe that is great for the trek from your stateroom to the pool or hot tub and back. Workout clothes, sun block, a good book for those lazy hours in a deck chair, all medications including something for motion sickness if you suspect any trouble should be included on your list.
Princess (and I assume most others cruise lines) provide hair dryers in all staterooms, along with soaps, shampoos, and body creams. Ladies might want to pack a shawl or light wrap, as even in the nicest weather, it might be cool for a late night walk on deck.
Pack a light weight backpack for carrying around cameras, bottled water, books, etc, especially for any shore tours - keep your hands free, your valuables safe and a place to keep your purchases out of sight.
On the last night of our cruise, all passengers were asked to place luggage outside their stateroom by 10:00 that evening. We packed everything except items needed for that night and the next morning. Be sure to take a small suitcase so that you can pack your toiletries, clothes from the night before, and last minute items. We were asked to leave our staterooms by 8:30 but were not scheduled to leave the ship until 11:00 and we didn’t want to lug around a large suitcase. On shore, you will be re-united with all your luggage.
Don’t forget to bring lots of film; it is quite expensive on the ship. Since no clocks are in the Staterooms, you may want to pack a small travel clock.