Other than the basics - clothes for each day, formal wear for formal night, shoes for the beach, etc :
At least 2 swimsuits - that way one can hang in the bathroom to dry while you wear the other.
Lanyard. I look for one that has a hook to hold the card instead of a pocket (since they have to swipe it) quick-release for the hook so I don't have to take it off over my head every time I purchase a drink, and a breakaway release in back. Here is a good example on Amazon.
Instead of trying to get a power strip on, check your electronics and see if they all use USB to charge. Then you can bring a USB multi-charger like this instead of dealing with all the plugs.
Backup battery/charger - poor signals and week wi-fi drain your phone batter quickly on shore (or if you use the shipboard Wi-Fi)
Go to the dollar store and pick up a $1 solid air freshener like a Renuzit. The bathroom will get funky after a few days and while a spray can is nice a constant freshener like this works better
A pop-up hamper or laundry sack to put your dirty clothes in. Or an empty suitcase in the bottom of the closet can do in a pinch - just keep it closed so it doesn't stink up your clean clothes.
Some small over the counter remedies. Aspirin, sea-sickness medicine, Pepto, tums, allergy medicine, mosquito repellent, sunscreen, etc.
Wrinkle release - there will not be an iron or steamer in your room for your formal wear.
Shout Wipe & Go Wipes (or similar) - because laundry is inconvenient on a ship, and a quick touch-up may be necessary for pictures after dinner
Underwater Camera - Yes, most people just use a waterproof bag on their phone. But since a phone nowadays is $900+ and an excellent 16mp Fujifilm underwater camera is only $175, I prefer to keep my phone in my bag instead of taking it snorkeling with me. As a plus, the camera has inexpensive removable media so it is easy to swap-out a card and keep shooting vs trying to empty out some room on your phone's storage.
Travel coffee mug - the small cup & saucer in the MDR is too small and unstable, and the paper cups are too hot. A travel mug is great for standing on the balcony and watching the sunrise in the morning.
Hangers - the thin metal ones you get from a dry cleaner won't take up much room. But since your cabin will only have 4-6 hangers when you get there you will need more to unpack your clothes. And the steward will only have what other guests have left behind in prior years, so don't count on more than a handfull from them.
Sheet of paper with your cruise ship, cabin, dates, and phone number on it. Just incare your bag gets separated from it's luggage tag, they know what cabin to take it to or (if it is after the cruise) who to call and claim it.