With the exception of Canada, citizens of Commonwealth countries need a passport valid for at least six months, a return ticket and sufficient funds. Canadian citizens need a passport or birth certificate and an identity card.
No visa is required except for citizens of Sri Lanka, Nigeria, Pakistan and Sierra Leone.
US citizens, including those arriving by cruise ship, need a passport, but a visa is not required for stays of up to six months. Passports may be expired if they have been for less than one year.
German citizens can stay for 90 days without a visa. Similar conditions probably apply to other Schengen countries.
Japanese citizens can stay for 30 days without a visa.
Since 27 May 2014, Chinese citizens can also stay for 30 days without a visa. However, this only applies for tourist purposes; to travel to Jamaica for any other reason, they still need a visa.
Most other nationalities require a visa.