As talk of a Greek exit from the Euro continues to gain steam, it’s worth noting that it’s not so easy to force a country to stop using a currency. There are many examples of “dollarized” economies, countries that adopt a foreign currency as legal tender. In fact there are six countries in Europe that are not EU members that use the currency as a primary unit of account. While four of these countries have formal agreements to do so, two do not yet continue to use the Euro. From Wikipedia:
The euro is also used in countries outside the EU. Three states—Monaco, San Marino, and Vatican City— have signed formal agreements with the EU to use the euro and mint their own coins. Nevertheless, they are not considered part of the eurozone by the ECB and do not have a seat in the ECB or Euro Group. Andorra reached a monetary agreement with the EU in June 2011 which will allow it to use the euro as its official currency when ratified. Under the agreement it is intended that Andorra should gain the right to mint its own euro coins as of 1 July 2013, provided that Andorra implements relevant EU legislation.Some states (viz. Kosovo,[note 7] and Montenegro) officially adopted the euro as their sole currency without an agreement and, therefore, have no issuing rights. These states are not considered part of the eurozone by the ECB. However, in some usage, the term eurozone is applied to all territories that have adopted the euro as their sole currency. Further unilateral adoption of the euro (euroisation), by both non-euro EU and non-EU members, is opposed by the ECB and EU.
To complicate the picture a little more, international economic relationships in Europe don’t start and stop with the EU and the Eurozone. For a look at the landscape, a diagram is below: