It's been 10 years since I last travelled to Europe, and I didn't have experience with the Euro. I hope this is not a stupid question, but if I were to take cash(Euros) out in say Belgium, would those same Euros be good in Italy, France, Germany, etc? I wasn't sure if they are good anywhere in the EU? Thanks.
They are good all over.
Yes, Euros from any country are good in any other country that is on the Euro. I have heard stories about how an occasional merchant will not take coins from another country, but I have never experienced it myself. If you do run into such a merchant, take your money elsewhere. Also, I believe that Finland has done away with the 1- and 2-cent coins, but that's a minor issue.
It's like with the State Quarters in the US. They have to accept the New Jersey one in Georgia and vv. The Euro is a single currency of 12 European countries. Cyprus and Malta will join on Jan 1st, 2008. As another poster mentioned, Finland actually ruled out 1 and 2 cent coins so there nobody has to accept them.
The Euro has made country-hopping much easier than in the past. However, please remember that England, Scotland, Wales and Northern Ireland use the Pound and not the Euro as their currency. I also believe that Switzerland does not accept the Euro.
The comment about Switzerland is correct. They are still on the Swiss franc.
All the countries you mention take the same euro. If you have a question about any others check http://ec.europa.eu/economy_finance/euro/our_currency_en.htm
Amongst EU members, Sweden, Poland, the Baltic republics, the Czech Republic, Slovakia, Hungary, Romania, Bulgaria, Slovenia and the UK do not use the Euro. Amongs the traditional "western nations", non-EU members Norway and Swizterland, do not use the Euro either.