[EtherCat]

Boats are slightly more difficult to break into than cars and slightly less difficult than homes (which is to say, not very difficult) Ive heard stories of boats being broken into, but overall it seems much less likely than a car or a home. Even if someone did steal your entire boat, theyd be making their escape at 6 knots or so, and could be caught by *any* powerboat. There are still real life pirates, but piracy is very rare in the Caribbean... if you were going to somplace like Indonesia you might want to be concerned, but for most parts of the world, the crime rate among boaters is much less than among shore-dwellers.
Ive never read up on the rest of the Caribbean, but the Bahamian Navy (which fulfills the function of navy and coast guard, and is supported by the US Coast Guard) has a reputation of being very competent and efficient.
There is a very informative discussion on carrying firearms aboard in the ''cruising'' section of this message board - in the US the laws of carrying aboard a boat are the same as for land - ie crossing state lines, it must be unloaded and in a locked compartment. The Bahamas requires that a firearm be declared when clearing Customs, along with the amount and type of ammunition, and a permit will be issued for it, explaining that it must be neither fired nor taken off the boat.

The chances of being involved in a violent confrontation aboard are certainly less than they would be in most US cities... there are scary things out there, but (with the exception of Pine Island) pirates arent one of them.