Whatever you want. Cruise lines offer shore excursions that you can purchase once onboard. Caribbean ports offer island tours, catamaran rides, golf, duty-free shopping, horseback riding on the beach or in the mountains, or just enjoy one of the world's greatest beaches. In Alaska you can walk on a glacier, pan for gold, ride a kayak, take a scenic flight, visit a totem pole village, enjoy a salmon bake, or go river rafting. Wherever you go there are historic sights, fun activities or interesting towns to stroll through.
Tours are strictly optional.
Tours offered by the cruise line are an excellent way to see the area sights with a reputable company, and the presence of a guide adds a lot to the value of the trip. Should for any reason your excursion return to the ship late, you would be secure in knowing that the ship will wait. And in some cases you can do them cheaper on your own. Of course there is some risk involved with these options. Should the port just not be of interest to you, staying on the ship is an excellent way to enjoy it without the crowds.