News sources have been reporting the euro is faring poorly because of problems in Greece [1-3], specifically the impending inability to pay off its debt. Problems with debt repayment and borrowing costs are growing worse. I don't know if it has reached terminal limits, but it sounds close.
Looking at the one year graph of the dollar vs. the euro, the trend line is headed in a southerly direction, but it remains squarely between the highs and lows for the year. This might not even be a diminution of the euro, but a strengthening of the dollar.
Say Greece does default on its debt, how would that affect the euro? National governments are an economic entity just like any individual or business—where income comes from taxes and is spent on government services. Governments contribute neither to the inventory (since all they provide are services) nor the money supply (central banks do that), so the stability of the Greek government has little to do with the amount of euro's in circulation, or what is for sale in euros.
Perhaps people are concerned the European Central Bank will monetize Greek debt to help them out, as a kind of charity. I anticipate that is highly unlikely, but I won't rule out the possiblity. Some commentators have even questioned the euro's viability if Greece defaults [2,4]. How this resolves will be informative since Greece will be one of the first of many dominoes to fall.
1. U.S. dollar, yen gain on Europe debt woes.
2. Greek financial crisis proves test for euro zone.
3. Europe debt fears sink euro.
4. Greece's financial crisis puts future of the euro into question.
UPDATE [2/11/10]: The European Union has pledged "moral support" to Greece, whatever that is, but no money. I'm sure the euro responded negatively, but this is good news for it.
UPDATE [2/14/10]: No love from Germany to Greece today. A poll of Germans showed a majority would rather see Greece expelled from the euro zone than to bail them out. Of course, the two events are unrelated—there is no requirement for Greece to be bailed out for it to keep using the euro. Greece though, may want to leave to create its own currency that it can inflate from within to support its spending. That wouldn't, however, forgive its debt in euros.
UPDATE [2/24/10]: Thousands of Greeks take to the streets today in protest of responsible government spending. Things get personal as Greece demands more money from Germany for the Nazi occupation of WW2. There have been suggestions over the past few days in the news media that Greece covered up the true state of its economic situation with the help of Goldman Sachs.