You can also get free alcoholic drinks at the Captains Party, the Past Guests Party, and the Art Auctions. Other than the fu-fu drink at sail-away those few free drinks cover all I need.
You can bring on a few canned / bottled sodas or waters. The steward keeps the ice bucket full in your room. I say a few, I saw one family take 3 cases of soda on. But 2-3 get me through the week.
On the Lido deck there are numerous self serve drink stations where you can get the juices, tea, and lemon aid everyone else has already mentioned. (Don't forget to look for the softserve ice cream and yogert stations too.)