"The Caribbean" takes in a wide swath. Are you referring to the Nassau/Abacos/Eleuthra region or the whole thing including Puerto Rico and the Dominican Republic?
If the first, it's all good, I've been thru most of it, the only caution would be fuel and water capacity, and navigational skills. Lots of skinny water, and Lots of Coral heads in unexpected places. Not much in the way of navigational aids. and NO Coast Guard. Their "Coast Guard" is a volunteer group known as BASRA, Bahamas Air Sea Rescue. Great group of folks, but not the US Coast Guard. Another consideration is when you plan to do this. Most of these islands are fairly close to one another 75 miles +/-, and aside from the Atlantic to Bimini run, and the tongue of the ocean from the Berrys to Nassua, it's pretty decent. However, the Atlantic to Bimini is 55 miles or so of big ocean, and some times, nasty seas, even worse for the 37 miles or so from the Berry's to Nassau. Water depth on this section is over 2 miles.
If you're thinking the whole thing, St. Croix, US Virgin islands, etc. you better have a really good sized boat, Diesel power, trawler or motor sailor and tons of nautical experience. The only high risk port of call is Haiti, and avoiding the territorial waters of Cuba.
As of 1/1/06 you'll need a currest US Passport for you and all passengers on board.
There are some really fine books on cruising the area, especially worth the price is the Bahamas Cruising Guide. Lot's of detail, marinas, services, local knowledge etc. Available at Blue Water Charts and most West Marine stores.