The Dow Jones industrial average plummeted as much as 369 points, or 2.6 percent, in the first two hours of trading. The average was on track for its worst decline in a year.
The Standard & Poor's 500 index fell as much as 40 points, or 2.8 percent.
Energy companies and bank stocks took some of the biggest losses. Both industries presumably would have faced lighter and less costly regulation if Mitt Romney had won the election.
Stocks seen as benefiting from President Barack Obama's decisive win rose. They included hospitals, free of the threat that a Romney administration would have sought to roll back Obama's health care law, and renewable-energy companies.
With the election over, traders' attention returned to an increasingly sickly European economy, dragged down by a debt crisis for more than three years. The 27-country European Union said unemployment there could remain high for years.
The European Commission, the executive arm of the EU, said that it expects the region's economic output to shrink 0.3 percent this year. In the spring, the group predicted no change.
For next year, the commission predicted 0.4 percent growth, barely above recession territory. It predicted 1.3 percent last spring.
U.S. stock futures were higher overnight after Obama cruised to victory. They turned sharply lower after the European forecasts and discouraging comments from Mario Draghi, president of the European Central Bank. European markets turned negative as well.
Now that the U.S. election has been resolved, it's natural for traders to focus on Europe's problems, said Peter Tchir, who manages the hedge fund TF Market Advisors.
What they're tuning in to, he said, is the failure of a major European summit last week and minimal progress on the issues that are holding the region back.
"People can only digest one or two stories at a time, and people had put Europe on the back burner" before the election, he said.
Obama's win followed a costly campaign that blanketed markets with uncertainty about possible changes to tax rates, government spending and other issues seen as crucial to the prospects of some industries and the broader economy.
As jitters about the election subsided, traders confronted an ugly reality: The so-called fiscal cliff, which will impose automatic tax increases and deep cuts to government spending at the end of the year unless the president and Congress can reach a deal.
That's no easy task for a deadlocked government whose overall composition has barely changed -- a Democratic president and Senate and a Republican House.
If Congress and the White House don't reach a deal, the spending cuts and tax increases could total $800 billion next year. Some economists say that could push the economy back into recession.
"Obama's re-election does not change the bigger economic or fiscal picture," Paul Ashworth of Capital Economics Ashworth, an economic research company, said in a note to clients.
Tobias Levkovich, a financial analyst at Citi Research, told clients Wednesday that a compromise on taxes and spending was likely in mid- to late January, but that stocks will probably fall in the meantime.
A deal early next year is much more likely "once the political class begins to negotiate realistically and as the consequences . . . are too costly for either party to ignore," he wrote.
About two hours into trading, the Dow was down 345 points at 12,921, dipping below 13,000 for the first time since Sept. 4. The S&P 500 was down 37 to 1,391. The Nasdaq composite index dropped 75, or 2.5 percent, to 2,937.
As traders streamed into lower-risk investments, the yield on the 10-year Treasury note plunged to 1.64 percent from 1.75 percent late Tuesday. A bond's yield declines as demand for it increases.
Stocks continue to hurt from lackluster third-quarter earnings reports, Tchir said.
"There's been this whole litany of things that have been dragging down the market for a while, earnings chief among them, and that's still out there," he said, adding that those concerns "play as much of a role as anything to do with the election."
Earnings have been relatively weak, with many companies reporting lower revenue and darkening expectations for the coming quarters.
With more than four-fifths of them having reported, companies in the S&P 500 index say earnings are up about 2 percent over last year, the lowest growth rate in three years, according to data from S&P Capital IQ.
Broad industries reacted to the election much as analysts had expected.
Hospital companies soared because of expectations that they will gain business under the health care law, known as ObamaCare. HCA Holdings and Tenet Healthcare leapt 7 percent, Community Health Systems 6 percent and Universal Health Services 4 percent.
With Obama seeking to restrain the growth of military spending, defense companies could struggle to win government contracts. Their stocks fell sharply: Lockheed Martin Lost 5 percent, Northrop Grumman 6 percent and General Dynamics 5 percent.
Among the 10 industry groups in the S&P 500 index, financial stocks and energy companies fell the most.
Banks figure to face tougher regulation in a second Obama term than they would have under Romney. JPMorgan Chase and Citigroup fell 4 percent, Bank of America and Goldman Sachs 6 percent and Morgan Stanley 8 percent.
The biggest losers were coal companies, which had hoped that a Romney administration would loosen mine safety and pollution rules that make it more costly for them to operate. Peabody Energy dived 9 percent, Consol Energy 7 percent, Alpha Natural Resources 13 percent and Arch Coal 11 percent.
Oil companies fell less steeply.
Alternative energy companies, especially solar manufacturers, outperformed the indexes on expectations that they will continue to enjoy generous subsidies. First Solar was roughly flat and Yingli Green Energy Holding edged slightly higher.
Trading also reflected the outcome of ballot measures decided in Tuesday's election. After two states approved the recreational use of marijuana for the first time, Medical Marijuana Inc., a company too small to be listed on major exchanges, surged 17 percent.