The following countries have no minimum legal drinking age for alcohol. Again, this is separate from the minimum age for buying alcohol.
This doesn't mean that beer is served at snack time in kindergarten — just that, for whatever combination of reasons, the state doesn't see fit to regulate people who consume alcohol beverages, only people who are buying them.
Usually, this hands-off approach to legal drinking ages applies to private situations, not out in public; lots of localities will have restrictions on, say, buying alcoholic beverages for young people in a restaurant or bar.
To give a sense of how legal technicalities shape the consumption of alcoholic beverages, and how it varies from country to country, take the case of Malaysia (No. 60 on our list). Malaysia recognizes Islam (which forbids the consumption of alcohol) as its official religion, but doesn't enforce Shariah strictures on all its citizens.
If you are a Malay citizen who is Muslim, your ID will specify this, and it will be illegal to sell you any alcohol. Other people can be sold alcoholic beverages if they are 21.