Whenever you kill a mob, you get a chance (default is 5%) to get its head, including player heads!

All mobs have this chance except for a few. Here are the mobs without heads.

Cat
Parrot

Rabbit

Spellcaster Illager (shouldnt appear in survival gameplay)

Tropical Fish

Different Sheep Colors

In future versions, admins will have more control + commands to help such as (not added yet):

/beheadchance <%> - changes the chance of getting a mob head, replace the <%> with a number between 0 and 100

/playerheads <on/off> - changes whether player heads drop or not

/mobheads <on/off> - changes whether mob heads drop or not

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Not Enough Heads