Actually the official hurricane season starts in May and ends in November, so anytime during those months you can be watching for a hurricane. I agree with the above poster, you are definetely safer on a ship than on land during a hurricane. Most of our cruises are during the fall and winter months. In fact we were on a ship in the Western Caribbean while Katrina was coming in, NEVER FELT IT, the only way we knew what was going on was watching the television in our cabin. Again we were on a cruise while Wilma was coming in...never felt it.
The worse that can happen is your itenirary could get reversed, you could skip a port or if a hurricane hits close to your port of embarkation, you might loose a day or more of your trip, but the cruiselines are very accomadating about refunds or credits...then again the absolute worse case is if you are on a ship while a hurricane is going on you might get a couple extra days at sea.
I always recommend that my clients purchase the travel insurance, this way no matter what happens you are protected.