There are so many activities to do on a cruise ship, the only problem you will have is deciding what to do. There are on board activities, port of call activities, age related activities, and special interest activities. Generally activities on board the cruise ship are free, but you have to pay for an on shore activity or excursion.
Most cruise lines have a children's program, divided by age group. Games and activities are age appropriate. Children can participate as much as their parents want them to. These generally include games, physical activity like using a playground or pool, and arts and crafts. Sometimes there are dances and social activities for the teen group.
Some activities involve more physical activity than others. There are ships that have pools, water parks, ice skating rinks, climbing walls and areas for golf (lessons or miniature golf). Skeet shooting off the deck is another option.
Arts and crafts are usually available for all ages. Some ships even have art fairs!
The on board theater will run movies, both general and adult oriented. Board games, bingo and keno are examples of more sedentary activities to engage in.
Some cruise lines feature lessons, all sorts. You can learn a foreign language, how to cook foreign fare or gourmet meals, how to play golf, poker or dance.
Spas provide massages, hair care, manicures and pedicures and other special types of treatments for the body. Think how good that would feel after dancing in the disco all night!
If you have a special interest or avocation there may be a cruise with it in mind. The sounds of the blues, or a family oriented cruise, or special cruises for singles.
Of course there are shows with all sorts of entertainment, comedians, dancers, magicians, or singers for example. Often there is a casino 24 hours a day. And then night clubs for dancing and merriment. If you consider eating a cruise activity, there is someplace to go almost 24 hours a day.