This very much depends on your itinerary.
When it comes to most Caribbean cruises, shorts/skirts, sundresses, pants, blouses, t-shirts, knit tops or polo shirts, and bathing suits are always a must. And maybe pack a sweater, lightweight windbreaker or a jacket for evenings of colder days.
For cruises in Alaska, we highly recommend good sweaters, a raincoat, and fleece. You should always bring some sneakers/rubber-soled shoes for all activities on the deck, and a swimsuit cover-up for colder areas on the ship.
Take note that in certain regions or while visiting to shrines or religious sites, more conservative attires can be required.
The majority of cruises have at minimum one formal evening. Cocktail dresses/gowns are normally worn by women, and men can wear darker suits and ties.
For more casual evenings, sport shirts with slacks and sport coats are perfect for men. Women may wear dresses or pantsuit/slacks with a top.
What Should I Wear?