Peaches, Depends. Really, that is a very hard and difficult questions to answer. To get the best deal always check with various air carriers in your area and look for their specials. I usually go to "Bestfares.com" or "Lowestfares.com", "Cheaptickets.com" and "Travelocity.com" and one of those will usually have the best fare and times and let you know if they are available. Where you book is up to you. Also check with your TA and see what the cruiselines have to offer. Remember that the cruiselines almost always includes transfers from the airport to the pier and back which is figure around $20 each way. Also be aware that unles you purchase air deviation you can get some pretty poor flight schedules. The up side is that the ship will wait a reasonable time if you are delayed onboard one of thier flights and won't if you aren't. Best thing to do is research, research, research, and then make a decision based on what you find out.
You can do much better getting your airline tickets yourself we just did and saved quite a bit. Then for $26 you can purchase what they call a transfer form Carnival which means they will pick you up at the airport take your bags and get you to the ship. Then when you return to port after your trip they will get you to the airport.
PLEASE if you are flying into miami take a cab, $20 each way not per person either. Who wants to have to walk two blocks toting your luggage, and then have to wait up to two hours for the bus to fill. BAD advice. Even if you fly into ft lauderdale you can take an airport express cheaper than CCL's bus, unless you are going solo...
There are pros and cons for which way you book your airfare. I have heard horror stories of people booking thier own airfare and then a flight getting delayed or cancelled. They were SOL!!! I also know that most cruise lines will wait for delayed flights if there are passengers on those flights that booked from them(Air/Sea packages). But then again, you don't know what your flight itinerary is until your tickets arrive about 10 days before you sail.
You should be able to get a better price booking a flight on your own, though. If you can fly in the night before it would eliminate the worry of missing the ship. And it is nice to be able to get good flight times. There is nothing more boring than sitting around an airport for 6 or 7 hours!! My last cruise I heard other passengers say that thier flights didn't leave until 8:00pm!! We got off the ship at 11:00am BORING!!!!!
I guess depending on where you are flying from and the airlines you will have to weigh out the good and the bad. If you are flying all the way accross the US you usually end up spending the night before the cruise anyway. Or if you don't have all that far to fly you might want to take the absolutely earliest flight out or a red-eye.
I have booked Air/Sea packages on my previous cruises. I am cruising in September and I have chosen to book my own airfare and fly in the day before(kind of an extended vacation). I am saving quite a bit of $$$$ that way.
Good luck and Happy Cruising!!