We started with Carnival on our honeymoon in October 2001. Only 3 weeks after 9/11, you can imagine the security mess in the travel industry. But we had no issues with Carnival. They treated us like royalty, and we had a marvelous time. The low fares and excellent service keep us coming back.
We have been on Carnival twice when hurricanes impacted our trips: When 3 hurricanes in a row hit Florida, our cruise was reduced to three days - and they were awesome days because Carnival made us feel like they appreciated our sailing with them despite the hardships. We also saw Carnival open up their ships at bargain-basement rates to accommodate Floridians who had no power or water at home. And we were well-compensated for our shortened cruise!
In 2009, we were on the Conquest, which sails out of Galveston, when Hurricane Ike hit that coast. Our cruise was over, but we couldn't get home. Carnival overnighted us in Cozumel while they found out what was going on in Galveston/Houston. Then we sailed to New Orleans and overnighted, so those who had homes in unaffected areas could get home. Carnival made internet & phones (free!) available for passengers to contact family and to take care of flight arrangements, etc. Guest Services also helped folks with that aspect. For those who lived in the affected areas and had no power (A/C) to go home to, Carnival offered to let us stay aboard for $10/day/pp - (the tips for the crew) until they could get us closer to Galveston. Although only 300 passengers remained onboard, they flew in entertainers, offered full dining room service for dinner and partial for other meals, and didn't skimp on anything to make the next 3 days bearable. Most of us knew that our cars were destroyed, and quite a few had little or no home to go back to. This was a nice respite, a chance to gather ourselves for what was to come. When we arrived at the Bayport terminal, after silently passing the massive destruction of Galveston on the way in, Carnival had it fully staffed, and our debarkation was painless.
This kind of dedication to the customer is what keeps us coming back every year.