London's FTSE 100 index was down 4.2% and Germany's Dax had lost 5.6%, while Wall Street's Dow Jones lost more than 4% in early trading.
Shares in some leading banks plummeted, with Barclays and Royal Bank of Scotland down more than 10%.
Analysts again cited reasons including worries about global growth, and the eurozone debt crisis.
As well as some worse-than-expected US economic data, markets were concerned about the exposure of European banks to the eurozone debt crisis.
The European Central Bank lent dollars to an unnamed eurozone bank on Wednesday, the first of its kind since February, and a further sign of worries within the eurozone economy.
In addition, a report in the Wall Street Journal said that the Federal Reserve Bank of New York had asked for more information about whether the US bank units of big European lenders have reliable access to funds needed to operate.
The Federal Reserve Bank of New York has yet to comment.
Meanwhile the spot price of gold hit yet another record high, up 1.6% on the day to $1,816.09 an ounce, as more investors moved their money into the haven currency.
'Negative tone'
One analyst described the mood in the markets as "fairly bleak".
"There is a general negative tone in the markets right now," said Kathleen Brooks from Forex.com.
"In the absence of any new information investors are more comfortable selling. This could weigh on markets for some time as there appears to be no immediate solution to the eurozone debt crisis and there are growing signs that the UK, US and Europe are on the cusp of recession," she said.
In the UK, Lloyds Banking Group also suffered sharp falls, down 9.5%, while HSBC Holdings lost 6.6%.
Barclays' shares have now fallen 51% over the past six months, with RBS down 53%, Lloyds 56%, and HSBC 29%.
In Germany, Commerzbank was down 5.3% and Deutsche Bank fell 4.3%.
France is one of a number of European countries where there is a ban on short-selling of shares in financial firms, where traders bet that their value will fall.
Despite this, some of France's biggest banks were down heavily, with Societe Generale down 7.3% and Credit Agricole dropped 4.2%.
US concerns
On Wall Street, Bank of America was the biggest faller, losing 7.2%.
US investment analyst Jack de Gan, chief investment officer at Harbor Advisory, said all eyes were on the European banking system.
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He added: "If there's stress in major European banks, it will affect US banks too."
US investor sentiment was also hit by a big drop in a closely watched guide to manufacturing activity in the mid-Atlantic states.
The Federal Reserve Bank of Philadelphia's business activity index slumped to -30.7 points in August from +8.2 points in July.
It is now at its lowest level since March 2009.
Grant Lewis, head of economic research, Daiwa Capital Markets, London, told the BBC that the Philadelphia index was now "at levels that point towards recession territory".
Official US figures also showed that the number of people claiming unemployment benefit rose by 9,000 last month to a seasonally adjusted 408,000.
Mr Lewis added that markets were now looking to Federal Reserve chairman Ben Bernanke's speech next week at the US central bank's annual meeting in Jackson Hole, Wyoming, for signs of the bank agreeing to additional quantitative easing (QE).
Under QE, central banks pump new money into the financial system to try to boost the economy.
Slow growth
This was the second day of big falls for some bank shares. Wednesday's sell-off had come after comments in support of a financial transaction tax from German Chancellor Angela Merkel and French President Nicolas Sarkozy.
The proposed Merkel-Sarkozy tax would be used to raise money to help bolster any future bailout funds.
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The two leaders also called on Tuesday for "true economic governance" for the eurozone in response to the debt crisis.
There are concerns that the debt situation in the eurozone, which has already led to bailouts for Greece, the Irish Republic and Portugal, will also engulf Italy, Spain and even France.
Traders saw Tuesday's meeting as another missed opportunity to tackle the crisis and calm the uncertainty gripping the markets.
"What we need is the likes of Angela Merkel and Nicolas Sarkozy to come up with some ways to fight these problems but they met again this week and all we got was talk again. What we need is action," market analyst James Hughes from Alpari UK told BBC News.
"We are still in that same situation that it doesn't take a lot of news to get the markets going," Mr Hughes added.
"The problem that we have in the moment is that fears are generating... big swings one way or another. Today it is a big swing lower and there is nothing to say we don't get another big swing higher in the next few days."
BBC
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