I think Mark_R has great priorities

The four scourges of the sea have always been:
Disease
Fire
Sinking
Starvation

Starvation and dehydration are unlikely to be an issue on a modern cruiser, however an issue with the kitchens or on-board desalination could cause shortages or a less exciting menu. I don’t think it would be worth hoarding food in your room, but I’d always have water and snacks on hand. (Perhaps in that grab bag beside the life jacket) ?

Sinking – I think that that’s been covered. Lighting would be important, if the ship is dark, it could be very dark with many internal passages etc. Know the emergency procedures and try to stay dry. Just remember that its women, children and me first …

Fire. Very few people die from fire, it’s the smoke. Knowing the exits, and perhaps a good light and even a smoke hood would be good. Act Quickly is the mantra, get to an open deck with your family and don’t go back for possessions (same for sinking).

Disease. By far the most likely disaster to befall a cruise. Sweeping gastro and flu are not uncommon on big ships. In the event of an outbreak you should pay careful attention personal hygiene and even be selective about food and drink choices. Well cooked is probably safer that uncooked foods. Food related issues may be more of an issue after several days at sea; the food being served will then be several days older than when it was loaded.
Having a personal first aid kit that can addresses: gastro, dehydration, sea sickness and symptoms of cold and flu is probably a good idea.
If you have personal meds you need them too, and as always, you need extras because you never know if your trip will be delayed and you could be stuck for a few extra days; engine or steering failures are not unknown as well as political issues or severe storms.

Related to disease is sewerage failure, plumbing blockage are also not unknown. Once again personal hygiene and appropriate medication are the solution, plus perhaps some potent air freshener, personally I like peppermint essence because it is a remedy for motion sickness, stomach upsets and is excellent at masking smells !

Sunburn is an issue for many folk, use a sunscreen. You may wish to take some meds to treat burns too.

For the adults on the thread: Sometimes folk become relaxed and carefree on a holiday. Some cruises are even designed for single people. You know where I’m heading … take the usual precautions !

The ship will have a dispensary and medical personnel, but you don’t want to rely on them if there is any kind of outbreak because they will quickly be overwhelmed by numbers. None the less you should find out where it is during your exploration and mapping of the ship.

One additional thing is to just be aware of what’s going on. Talk with people and keep a check on the people around you, if they all start missing meals or you stop seeing them around, they may have simply changed their routine, or perhaps they have been taken ill ?