As of right now, passports are not required for US Citizens for cruises that start and end at the same US port. However, they are strongly recommended. While you do not need to have a passport to cruise to many destinations from the US, you do need to have a passport to fly home if there were an emergency. You can probably still work it out without a passport, but it will take much more time and in an emergency time is not always available.
The passport card is not as good as a passport book and you will also not be able to fly home from a foreign country with the passport card. If you choose not to use a passport or a passport card, a certified copy of a birth certificate plus a government issued photo ID for everyone over 18 is required.
When cruising to a foreign disembarkation port or a cruise that starts and/or ends outside of the US, US Citizens are required to have a passport. Your passport must be valid for 6 months after your cruise ends for many countries. You will also want to know if there are separate requirements for your ports of call. Some ports of call will have strict guidelines and laws pertaining to visitors. For instance, visitors to St. Petersburg Russia are required to have a visa, and we don’t mean the credit card. Most cruise lines will include the visa with the shore excursions they offer. Outside shore excursion company may or may not do the same. You will not be permitted off the ship if you do not have the proper documentation.
There also may be other rules or regulations you should be aware of. Also in Russia and Cuba, you cannot legally take local currency out of the country. If you convert your money when you arrive, you will not want to convert more than what you actually will spend.