The bank is the first major British financial institution to be hit severely by the global credit crunch sparked last month by a crisis in the US subprime, or high-risk, mortgage sector.
Saturday's newspapers showed pictures of customers crowding outside Northern Rock branches nationwide to withdraw their savings.
Thousands more jammed the bank's phonelines and website to try to get their hands on their money, raising fears that a "run on the bank" could exacerbate problems.
There were reports that about a $2bn had been withdrawn so far.
Fiona Howard,a former hotel owner, said: "Everything we have in our lives is in there. We would be left with nothing if it is lost."
Another customer, Tony Looch, 68, said "my confidence is shattered".
Appeal for calm
In an editorial, the Financial Times newspaper said: "The throngs of anxious depositors outside its branches yesterday show how quickly financial panic can spread.
"A crisis requires fine judgements and the Bank's decision to act, assuming it did not respond to political pressure, looks reasonable."
However, the daily said the Bank of England should charge Northern Rock a sizeable penalty rate and tide it over until it could be sold.
Shares in Northern Rock, which issued a profits warning on Friday, plunged 31.46 per cent to 438 pence at the close, dragging the European banking sector lower as investors fretted over potential difficulties elsewhere.
However, most analysts forecast that the troubled bank was very unlikely to go bust.
The UK's financial regulator, the Financial Services Authority, has appealed for calm.