It all depends on your risk tolerance and potential risks associated with your trip as well as cost. Keep in mind, passports for children under 16 are only good for 5 years. As others have said, if you are a US citizen on a closed loop cruise, a birth certificate will suffice.
We have passports because we are the type of family who always has some sort of emergency while on vacation and our 11 year old son has major medical problems. So, for us, the risk was too high and we opted for passports.Yes, emergencies happen but I have been on 15 cruises and none of us have ever needed to fly home from a foreign port, thankfully.
If you do have an emergency and need to fly home you would have to get an emergency passport first.