The euro is facing its first major crisis. Even after a 750 billion euro bailout for Greece and other troubled euro zone members, the currency has fallen to its lowest level against the dollar in four years. Many analysts say the euro has much further to fall — with some hardcore pessimists predicting it could disappear entirely. Does the euro really face extinction? (Watch an Al Jazeera report about the euro's collapse)

No, this is just a healthy correction: The euro has long been overvalued against the dollar, say Paul Betts and Peter Smith in the Financial Times, and a weaker currency could actually help save the eurozone economy. Not only will it "bring down European government debt ratios," it will also "help exporters of goods and services" and could even "stem the steady trend of industrial groups" moving offshore to "lower cost countries."
"The falling euro is a luxury Europe can well afford"

Yes, weaker members might kill the currency: The euro is on the brink of collapse, says Kurt Brouwer in Market Watch. At some point, economically battered countries like Portugal, Italy, and Spain will choose to escape the "euro straitjacket" in favor of the freedom of managing their own currencies. When that happens, there won't be "much reason to keep the battered euro going." 
"Is it the euro or the Yugo?"

Or the strongest member might do so: German voters are already fed up with being forced to underwrite the $1 trillion Greek bailout, says Lou Brien in World Market Media. So it's unlikely that country's leadership has much patience for throwing good money after bad in order to keep a bunch of spendthrift neighbors out of bankruptcy. And without Germany, there's no euro.
"The euro is in trouble"