When cruising in the Caribbean, I leave it in the safe. Water activities really don't lend themselves to being practical with carrying it around. Plus, it definitely would be much easier to make arrangements to get home from there should I miss the ship (which I vow never to do!!) When I cruise overseas such as to the Med however, I take it to port with me in case of emergency (on cruise about 35 people missed the ship due to a traffic jam from Paris to the pier. The ship left without them)

When I travel on a land based trip I will generally leave it in the safe of the hotel.