Stock prices plunged Thursday in the US as well as Europe amid growing worries about financial contagion from the Greek debt crisis.

The Dow Jones Industrial Average fell 347.8 points (or 3.2 percent) Thursday, while European stocks were down nearly 5 percent - the third straight day of declines with Greece in the spotlight.

Thursday's trading centered around the fear of ripple effects on several fronts.

They include:

• Virulent and sometimes-violent street protests in Athens showed a rift between many Greeks and their government. The parliament voted to support austerity measures designed to win international rescue loans. The underlying question: Will the Greek public go along with belt-tightening that could be the equivalent of a multiyear recession for that country, or will Greece eventually default on its debt and drop its membership in the euro zone?
• The euro fell as Jean-Claude Trichet, president of the European Central Bank (ECB), expressed confidence that Greece would not default on its debts but offered no new steps to quell investor doubts. The underlying question: With bond investors betting that Greek debt is still at risk of default, does the ECB have the tools or the will to calm the atmosphere of crisis?
• Moody's, the credit-rating agency, issued a report warning that banks in Portugal, Italy, Spain, Ireland, and Britain could all be weakened because of the debt crisis. The underlying question: With several European nations in fiscal trouble, will the burden of sovereign debts spill over to affect the health of private-sector banks and the wider economy?
• Germany's parliament is preparing for a Friday vote on granting aid to Greece. The underlying question: Will Germans be willing to pay a significant price - helping Greece and possibly other euro zone nations - for the economic benefits they reap by preserving Europe's currency union?

"Trichet keeps insisting that the Greek economy constitutes only 2 percent of the European economy," economist Desmond Lachman of the American Enterprise Institute wrote in a Thursday commentary for the institute. But "the body blow that a Greek default would deliver to the European banking system - together with the contagion that it would unleash on Spain, Portugal, and Ireland - would have major reverberations throughout the global economy."

The path forward

That potential for contagion has taken center stage for investors this week. The common theme in all this is uncertainty, which translated into a sell-off in financial markets.

Many finance experts say the logical path forward is for Greeks to adjust their living standards downward, for citizens of other high-debt nations to do the same, and for nations like the Germany and the US to support aid packages from the International Monetary Fund (IMF) to help Greece make the transition while remaining in the euro zone.

But Germans are angry at having to bail out another nation, just as many Greeks are angry at the belt-tightening that's being imposed on them as the price of membership in the currency union.

Even if Greeks go along, there's no guarantee that investors in Greek bonds will get their money back.

Europe's PIIGS

Here's why all this is more than just a localized problem.

After Greece, the euro zone may have to deal with debt worries among the rest of the so-called PIIGS nations (Portugal, Ireland, Italy, Greece, and Spain). Private-sector banks in Europe hold lots of bonds from these nations, so the risk of default adds to worries about their health, too.

At the very least, the chaos raises concerns that Europe's economy will be in the doldrums, and that the global economic recovery will be dampened as a result. US and Asian firms won't be exporting as much to Europe.

At worst, the turmoil leads some investors to believe that difficult political decisions will be needed to keep the euro zone alive. (The euro has fallen this year from being worth about $1.45 to $1.26 on Thursday.)

Mohamed El-Erian, who heads bond-trading giant PIMCO, told CNBC that he sees a "high probability that euro zone will look different a year from now," with new rules, fewer members, or both.