Penny is mostly correct. One exception that always sneaks in under the radar (I had forgotten about them too) is NCL. They will allow 18 year olds to drink beer and wine, but only in certain cases and with permission of an "accompanying" parent or guardian who is at least 21 years old. In the case of the guardian, a permission form needs to be completed by the parents.
So, in a nutshell...
You need at least a couple of 21 year old designated guardians going with you since you have to be in a cabin or adjoining cabin with someone who is 21 or older. With the exception of Hawaii and Alaska cruises you can drink once in international waters provided your guardians have gone to guest relations on the ship and approved you for alcohol.
Even without the alcohol consent, you still need permission slips from parents just to go on the cruise.
For Carnival, Royal Caribbean, and the other mainstream lines, you have to be 21 to drink and the accompanying guardians have to be 25.