All penguins except Ninja Penguins drop 0-2 skins on death. Each penguin drops a skin according to its color:

The penguin skins can craft many items, listed here:

All the penguin skins can also be used in place of leather to craft books and item frames.

Note that if you hit, kill, or try to shear a penguin that is not tamed, all other wild penguins around it of the same species will attack you, although you can pacify them by feeding them raw fish. Flame Penguins will attack you by default unless you are wearing a full set of some kind of penguin armor. For more information on Flame Penguins' behaviour, see the main article. There are a few exceptions to this rule, though: Cloud Penguins will run away rather than attack if they sense you as a threat, and  Ninja Penguins attack you regardless of what you do.