I just returned 7/20/03 from Rhapsody of the Seas (RCCI) and we took our own 12 pack of soft drinks. The cabin steward volunteered to provide us an ice bucket specifically for icing down a few cans at a time.
You DO have to pay for each soft drink when buying them individually from the cruise line. If you buy a drink card, you get a small glass of soda but for $1.50 (plus 15% gratuity) you can buy a can of soda.
Drinks cards cost $20.00 for 17 years and under, while $30.00 for adults.