The worst case envisions governments defaulting on their debts, a run on European banks and a worldwide credit crunch reminiscent of the financial crisis in the fall of 2008.
A Greek election today will determine whether it happens. Syriza, a party opposed to the restrictions placed on Greece in exchange for a bailout from European neighbors, could do well.
If Syriza gains power and rejects the terms of the bailout, Greece could lose its lifeline, default on its debt and decide that it must print its own currency to stay afloat.
No one is sure how that would work because there is no mechanism in the European Union charter for a country's leaving the euro. In the meantime, banks and investors have sketched out the ripple effects.
They think the path of a full-blown crisis would start in Greece, quickly move to the rest of Europe and then hit the U.S. Stocks and oil would plunge, the euro would sink against the U.S. dollar, and big banks would suffer losses on complex trades.
In the worst case, Greece's exit starts off messy.
The government resurrects the drachma and says each drachma equals one euro. But currency markets would treat it differently. Banks' foreign-exchange experts expect the drachma would plunge to half the value of the euro soon after its debut.
For Greeks, that would likely mean surging inflation -- 35 percent in the first year, according to some estimates.
Greece's government and banks currently survive on international loans, and if it dropped the euro, the country would probably be locked out of lending markets, said Athanasios Vamvakidis, foreign-exchange strategist at Bank of America-Merrill Lynch in London. So the Greek central bank would need to print more drachmas to make up for what it could no longer borrow from abroad.
That's one reason analysts say the switch to a drachma would lead the country to default on its government debt, possibly triggering losses for the European Central Bank and other international lenders.
Most assume foreign banks would have to write off loans to Greek businesses, too.
European banks would take a direct blow. They've managed to shed much of their Greek debt but still held $65 billion, mainly in loans to Greek corporations, at the end of last year, according to an analysis by Nomura, a financial services company.
The European Central Bank and European Union would have to persuade investors in government bonds that they will keep Portugal, Spain and Italy from following Greece out the door. Otherwise, borrowing costs for those countries would shoot higher.
The main way European leaders have tried to calm bond markets is by lending to weaker governments from two bailout funds. Experts say these two funds, a financial firewall to stop the crisis from spreading, need more firepower.
Much of the 248 billion euros left in one of them, the European Financial Stability Facility, was pledged by the same countries that may wind up needing it, Vamvakidis says.
"If they fail to reassure bond investors, all of the nightmare scenarios come into play," said Robert Shapiro, a former U.S. undersecretary of commerce in the Clinton administration.
The biggest danger is known in financial circles as contagion.
"It's like a disease that spreads on contact," said Mark Blythe, professor of international political economy at Brown University.
The bond market, where banks, traders and governments cross paths, provides the setting. If Greece dropped the euro, traders would become more suspicious of Spain, Portugal and Italy and sell those countries' government bonds, pushing their prices down and driving their interest rates up.
Higher borrowing costs squeeze those countries' budgets and push them deeper into debt. Plunging bond prices also would imperil Europe's troubled banks. The banks are big holders of government bonds, which they bought when the bonds were considered safe.
At this point, the risk would be high for a run on banks throughout Europe. People would worry that the banks might fail and would rush to withdraw what they could. Analysts and investors say that's the biggest fear.
In less frantic times, the government would come to the rescue with cash or take over the banks. But all this is happening in the middle of a government debt crisis, and if the crisis gets worse, the Spanish or Italian government couldn't raise enough money in the bond markets to save the day.
"They can't afford to guarantee deposits or money market balances," Shapiro said. "They don't have the ability to borrow internationally from bond markets. Where are they going to get the funds?"
From here, the crisis could get much worse: Banks could fail, the surviving banks could stop lending to each other, and a credit freeze could shut down commerce in Europe as assuredly as a blizzard did last winter.
One way to stem the contagion would be to create so-called eurobonds -- bonds backed by all 17 countries that use the euro. They could be sold to raise money to buy the bonds of troubled European governments. With the backing of 17 countries, including mighty Germany, eurobonds would have a yield far lower than the bonds of countries like Spain and Italy.
The crisis would cross the Atlantic through the dense web of contracts, loans and other financial transactions that tie European banks to those in the U.S., experts say.
Blythe, the professor at Brown, believes credit default swaps, the complex financial instruments made infamous by the 2008 financial crisis, would provide the path.
Banks created the swaps to sell as insurance for loans. After lending money to a business or government, investors can turn to a bank and take out protection on the amount they lent. If the borrower runs into trouble and can't pay -- say, the government of Spain defaults -- the banks that sold the insurance cover the loss.
It's not clear how much U.S. banks have at risk to Europe through credit default swaps because regulations let banks keep that information a secret.
"You could have American banks up to their necks in CDS liabilities," Blythe said. "We don't even know."
So what's the good news? It's hard to find anybody who believes the crisis will get that far.
The bankers planning for a Greek exit from the euro say they think European leaders will get scared into action. The Federal Reserve and other central banks learned from the financial crisis in 2008, they believe, and will jump in to stop the nightmare scenario from unfolding.
Just in case the worst comes to pass, analysts at Barclay's have attempted to estimate the fallout. They say it would be like the days after the investment bank Lehman Brothers collapsed in September 2008. This time, they project that oil would fall to $50 a barrel, stock markets outside of Europe would plunge 30 percent, and the dollar would soar to trade nearly even with the euro.
Blythe is skeptical that it will get that bad because he hopes the previous financial crisis has left governments and central banks prepared.
However the Greek story ends, Blythe believes it's bound to be ugly.
Putting 17 countries together to share a common currency worked well when Europe prospered. Now that they're struggling, "all the design flaws are becoming apparent," he said. And every solution that's supposed to fix a problem creates another problem.
The proposed $125 billion loan to save Spanish banks, for instance, will add to the debt burden of Spain, which sent its borrowing costs higher this week and will put a tighter squeeze on its budget.
"The euro itself," Blythe said, "is a bloody doomsday machine."