Take a look at the Caribbean section of Noonsite.com "Countries" page. Here's a link...
As skipmac said, it varies by country. I've sailed to all but three of the eastern Caribbean
countries. You will have to clear in through Customs
and Immigration at each country. They will ask you how long you want to visit, and most will grant you a 30 day Visitors' Visa, if you ask for it. Fees
will vary. The cruising guides
will have information on where to go to clear in, office hours, etc.