Sorry to disagree, but not all BBs work everywhere. I have a BB, and it will not work in Europe according to Sprint.
Regarding the Caribbean, I don't know, but your provider will. The phones will work in Puerto Rico and the USVI because they are US territories and on US plans.
BTW. . . Sometimes, even if the phone will work outside of the US, you will have additional fees because they are not US territories. For example, I asked about iPads working in Europe since some have the 3/4G technology and was told that they would work there, but that I'd have to pay extra for the data because it's out of the country.
As CF said, check with your provider as they'll know which model you have and whether or not it will work and whether you're going to have to pay high fees anyway.
Read and post cruise reviews
Veracruz - '85
CCL Tropicale - '94
RCCL Adventure of the Seas - '05
CCL Valor - '06
CCL Victory - '06
Celebrity Century - '07
CCL Triumph - '07
CCL Victory - '08
NCL Gem - '10