No, you *aren't* required to give a credit card. You can make a cash deposit on your sign and sail instead. Or you can use a VISA or MC check card.
You didn't mention which ship you were sailing, but on Carnival, tea, lemonade, punch and coffee are free at meals.
If you are a big soda drinker, consider purchasing a soda card. Unlimited soda (one person per card) for the entire week at about $4 per day.
Carnival Elation March 11
Carnival Imagination Sept 07
Carniival Sensation Dec 06
RCI Sovereign of the Seas Sept 06
Carnival Miracle Sept 05
Carnival Glory Sept 04
Carnival Fantasy Jan 04