This June marks the 10th anniversary of the creation of National Caribbean-American Heritage Month.
There are plenty of great resources online to help you find your ancestors in the Caribbean. Here a few:
Caribbean Genealogy Research
Includes lists of country-specific resources, records depositories, and a surname index.
Caribbean Family History
Databases of burials, religious records, and slave compensations primarily for Barbados.
Cuban Genealogy Center
Links for Cuban genealogy records.
Genealogy of Jamaica
Information and online resources for Jamaican genealogy.
Puerto Rican Hispanic Genealogical Society
Articles and resources for research in Puerto Rico.
You can also search FamilySearch's collections for the Caribbean: Anguilla, Antigua and Barbuda, Aruba, Bahamas, Barbados, British Virgin Islands, Cayman Islands, Cuba, Dominica. Dominican Republic, Grenada, Guadeloupe, Haiti, Jamaica, Martinique, Montserrat, Puerto Rico, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Trinidad and Tobago, and the US Virgin Islands.