Soda & water are fine, but according to Princess' policy, only wine & champagne are allowed to be brought onboard. However, that being said, it seems the policy is not evenly enforced on all ships - on the Regal last April/May, I was allowed to openly carry beer onboard at several ports.
I just noticed on the Princess site that they state there is a location on board each ship where you can purchase alcohol for consumption in your cabin. I take it that this would be at a very inflated rate???