Nearly all of the puffball mushroom species are edible, but not all. No varieties of the puffball mushroom are poisonous, and the inedible species are easy to identify. If the mushroom in question has no stalk or gills and is solid white, it's edible.
The Stalked Puffball-In-Aspic and the Beaked Earthstar are two members of the puffball family that are inedible. The former is covered in jelly, and the latter appears to have a starfish-like stool it sits on. The Destroying Angel mushroom is not a part of the puffball family, but it does look similar to the puffballs and is a fatally poisonous mushroom, told apart by the presence of gills inside when cut in half.