Barbados requires a passport (starting March 1st). I know of no other islands that require one, (at least for cruise passengers, Grand Cayman requires one if you are not on a cruise ship).
That being said, I recommend that everyone get a passport. Not only is it more convient than keeping track of a birth certificate etc. If you do have problems, being able to instantly prove your citizenship at the your countries embassy or consulate, is worth the price.
I actually take both, I keep the birth cert. in my carry-on bag, just in case my passport is lost or stolen.
Chuck
