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Why could the serious financial woes of some EU member states lead to the end of the Euro?
The Euro is a common currency between various countries in Europe.  This means that individual countries give up their traditional sovereign control of their own currency, and cede that control to the EU. Such a system has many advantages, but it also means that individual countries cannot deal with their unique situations as easily.  For instance, if the US were a part of the EU, then the Fed couldn't issue $600B the way they are to bolster the economy. The danger to the Euro is that countries will withdraw their participation in order to micromanage their economies more effectively.  If a major country withdraws its participation, it could start a domino effect where many countries withdraw so that they too can manage their economies more effectively.  As more countries withdraw, a shared currency becomes less and less appealing.