This is a topic upon which I became familiar as I just returned from Germany. There may be one currency for most of the European nations but there certainly isn't one SIM card that will work in these same countries. What a stupid inconvenience. Vodaphone, O2 and others may be in many countries but it doesn't mean that you can buy one SIM card that covers all of those countries.
One SIM card for the EU...why isn't there one? My SIM card on my American phone certainly works in Canada. So why is it so backwards in Europe?
These SIM cards can be expensive and then you have to buy a prepaid plan for each country. Perhaps pick just one country.