Members of the Eurozone were allowed to use the Euro. See the list on Wikipedia.
Liechtenstein doesnt use the Euro they use the Swiss Franc simply because they have do not want to use the Euro. Its like asking why Canada doesnt use the American Dollar, or why New Zealand doesnt use the Australian Dollar, they have their own currency they use.
Hungary does not use the Euro but you can Exchange the Euro at a bank.
Norway does not use the Euro
Morocco doesn't use Euro
Euros
The currency of Italy is the Euro (€).
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No china does not use the Euro. The currency in China is the Renminbi.
Albania does not use the euro. Albania's currency is the Lek
No. Switzerland and Liechtenstein do not use the Euro.