Hurricane season is from June until 1 Nov BUT, the great thing about cruising as opposed to land vacations, (or one of the many anyway), is that shouod a storm threaten then the ship just changes intinaries. Last year was the first year that I can remember when a couple of cruises were actually cancelled due to weather and that was the 3 day stuff to the Bahamas and one of the Bermuda cruises simply because Floyd was out there just floating around and there was nowhere else for these cruise ships to go. The Caribbean just goes the other way. Can it happen, yes, but the chances are rather slim and the prices are very low at that time of the year because there is that slim chance.
The weather in the Caribbean is beautiful and consistent, give or take a few degrees in temperature, all year long. The weather is typically more humid in the late summer and fall. The hurricane season officially lasts from June 1-November 30, but the peak seems to be August-October. Last year, there was at least one hurricane as late as mid-November. The great thing about traveling during this season is that prices are lower and if you're traveling without children, there are fewer kids onboard once school starts.
Winter is a great time to go if you live in a northern city and want to warm up, but prices are higher and chances of flight cancellations due to snow and ice are much greater.
Spring is also a good time weather-wise, but many ships start repositioning as early as April from the Caribbean to their summer homes in Europe and Alaska. And then there are those rowdy spring-breakers!
As far as I'm concerned there's no bad time to visit the islands, and I'm sure you'll have a great time whenever you decide to go.