Yes, I have been on 2 cruises that were affected (and I had one canceled due to Katrina)
You can't really say for sure how a cruise is going to be affected until you are on the ship. There are a couple of ways a cruise can be affected. All of them revolve around the fact that the captain will keep the ship away from danger.
1) your cruise is canceled or delayed because the ship can not get into port to finish the previous cruise and embark the new passengers because it is out at sea while the storm is in or near the port. This is the worst case scenario. Example- we were scheduled to cruise in October out of Galveston. Katrina came in and Carnival gave up our ship to be used as a hotel for victims. They canceled our cruise. But since the Conquest was moved out of NO and into Galveston we were allowed to rebook on it.
Of course the reverse of that is true also. If you are out on the ship and it can't get back into port.. then FREE EXTRA CRUISE DAYS!
2) your itinerary is changed up. We were on a western Caribbean cruise going to Cozumel, Jamaica and Grand Cayman and a small Hurricane was going through those islands. We got on board to find that they reversed the itinerary and went to Jamaica first and basically followed behind the hurricane. Or some ships do an eastern Caribbean one week and then a Western the next.. if need be they will just do two of the same back to back depending on the storm track.
3) You just miss a port. If the ship can't get to a port because a storm is near, then they just skip it altogether. Sometimes you get a cruise to nowhere.
If you can get on your cruise, at least you will go somewhere even if its just sea days. The captain will not put the ship in any danger and the ship can out run a hurricane if need be, so you will still cruise, but you are not guaranteed to cruise to where you thought you were going (of course that is true on any cruise)
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013