Before you start packing sunscreen and bathing suits, make sure you remember your airline tickets, cruise documents, passport and any necessary travel documents such as travel visas and vaccination certificates. It is a good idea to make copies of these documents. Also remember to bring emergency contact information, medical insurance information and a list of any prescription drugs you may be on. You may also want to bring a pre-paid phone card if you want to call family and friends while you're away.
For while you're on the ship, you might want to bring a book to read on deck or some cards and travel board games to play with your companion. If you're sailing through an area where you might see marine life, pack a pair of binoculars as well as a camera (with extra film or a memory stick). Don't forget your sunscreen---even if you are not going on a tropical cruise, you are likely going to spend a lot of time on deck and will need sun protection.
Research how formal the dining rooms are on your cruise---some require special dinner wear. Other than that, pack for the climate you're traveling to. Don't forget to bring a sweater---even if you're in the tropics, the ocean breeze can be cool at night.