First uses of Euros as official currency:
The first Euros in January 1, 2002 were spent in the island of Reunion (a French island in Indian Ocean). Mayor of Saint-Denis, Rene-Paul Victoria, bought fruits, for high price of 0.75 €/kg.
In Europe proper, Finland and Greece, being the eastmost countries, were the first countries to move to the new year - and to the new currency.
In Helsinki, Finland, the Minister of Finance Sauli Niinistö made the first purchase with Euros - a cup of coffee for 1 €.
Meanwhile in Athens, Greece, Prime Minister Costas Simitis withdrew the first Euro banknotes from an ATM. (Niinistö then called him, saying they would be the best people in future EU meetings to talk of Euro issues because they are obviously more experienced Euro users than others =)
(Sources: Yahoo! news, Euronews and the live TV program from Helsinki)
The Finnish euro coins have nature-related patterns (1 € coin has flying swans, 2 € has cloudberries); the eurocent coins have the traditional Finnish heraldic lion.