from the Carnival web site:
Are there any age restrictions on board?
Drinking Alcoholic Beverages:
Guest must be 21 years of age or older to be served alcohol on board. Proper I.D. with birth date is required.
From my experience, this is being inforced the way it is written down. My younger brother (who is 25 and doesn't look younger) had to present proof of age quite a few times on the "Carnival Liberty" this summer - even when he wanted to order a beer with his dinner. For him as a German this was quite unusual (he found it annoying first, later amusing) as here in Germany you are allowed to drink beer from the age of 16.