John F. Kennedy, LaGuardia and Newark airports all offer direct flights to the Caribbean. LaGuardia is the most limited, but from here you can fly nonstop to Montego Bay, Jamaica, Ponce and San Juan in Puerto Rico, and Santo Domingo, Dominican Republic. The other two New York area airports, Kennedy and Newark, offer a wider range of flights all over the Caribbean, and you can get to almost any island via a direct flight.
George Bush Intercontinental Airport and William P. Hobby both have direct Caribbean flights from Houston, with Bush offering the lion's share. Fly to Bonaire, Puerto Rico, Aruba and Jamaica, among other islands. Note that some direct flights only operate one or two days a week. On the other days, you have to change planes. Also, there are additional direct flights at holiday times. Continental, based in Houston, is your best bet for Caribbean travel.
Miami International Airport offers hundreds of direct flights every week to almost any Caribbean island. This is great news if you happen to live near Miami; if you live elsewhere, you may find yourself changing planes at the vast airport. If you are coming from the West Coast, which offers few direct flights to the Caribbean, you will likely change planes here. US Airways offers the most direct flights from Miami to the Caribbean.