Greece's economy peaked in 450 B.C., but its sway over world financial markets might be reaching a new high.

Regardless of the recent election results, no one knows what will happen to Greece in the coming weeks and months. It might rebuild. It might collapse. It might leave the euro. Or something totally unforeseen could happen.

No one knows. All we know is that the weakness of the country's economy and the dysfunction of its government are breathtaking.

What’s in store?

Here's a simplified version of what's keeping people worried.

If Greece balks at the conditions of its bailout, it could be pushed out of the euro currency and back to its old currency, the drachma.

That could change everything.

A key tenet of the euro pact is that you join, and you're in for life. You follow the rules, and you work with other nations to solve your problems.

Greece leaving the euro would throw all that out the window, which means a couple of things will likely happen.

First, the new drachma would be worth much less than the euro, and Greeks and the country's bondholders would lose a substantial portion of their savings — estimates of devaluation range from 50 percent to 70 percent. All debts, contracts, and obligations would likely be redenominated into the new currency. This would almost certainly happen over a weekend when banks are closed, and a bank holiday would likely be arranged to minimize chaos and allow the government and banks to sort out the details.

Stopping the flight of cash

Capital controls would likely be put in place to prevent money from leaving the country, and perhaps even border patrols to make sure citizens aren't literally fleeing with bags of cash. The government may set a favourable exchange rate linked to the euro, and promise to implement a slow, gradual exchange for new drachma.

Even with detailed preparation, this would be an ugly process. Products Greece imports - things like fuel, medicine, and machinery - could face drastic shortages as businesses can't pay invoices denominated in euros. UBS estimates that Greece's GDP could fall 50% if it leaves the euro. Everyone expects riots and social chaos - what do you have to lose when you're unemployed, have had your life savings wiped out, and have lost all hope?

And that's just Act 1.

What about the next domino?

If Greece exits the euro, suddenly lenders look at Spain, Italy, Ireland, and Portugal with doubt. If Greece can leave, maybe they will, too, the thought goes.

Scared that other countries will revert to new, weaker currencies, creditors demand higher interest rates, or cut countries off from funding altogether. After watching Greek households lose their life savings, depositors in other countries start pulling their money out of banks and hiding it in the relative safe havens of France, Germany, and the underside of their mattresses.

Both of those actions mean European banks become even more loathe to lend, worsening the Continent's economic problems, which increase worries that more countries will default and exit the euro, spiralling on and on.

The one thing capable of stemming a banking panic - a sincere government deposit guarantee - isn't feasible in many weak European countries because their government's treasuries don't have the trust of bond markets. Banks may not be able to count on the European Central Bank for liquidity because their assets might not be strong enough to post as collateral.

Existing bailout funds aren't large enough to make a measurable difference, and Germany seems unwilling to sacrifice for its profligate neighbours more than it already has. That's where things get real hairy: The rule of thumb with financial panics is that they spread until stopped. In Europe, there's not much capable of stopping them.

Foolish take-away

That's the worry, at least.

Realistically, the biggest risk is something no one foresees. There's chatter that Greece leaving the euro could bring about something like the aftermath of Lehman Brothers' bankruptcy in 2008, but that's the wrong way to look at this. As New York Times reporter Binyamin Appelbaum wrote recently, "The next crisis is never like the last one."

If you’re in the market for some less risky, high yielding ASX shares, look no further than Secure Your Future with 3 Rock-Solid Dividend Stocks. In this free report, we’ve put together our best ideas for investors who are looking for solid companies with high dividends and good growth potential. Click here now to find out the names of our three favourite income ideas. But hurry – the report is free for only a limited time.