Almost 10% of adults - more than 4m people - in Britain say they have responded to a scam in their lives, the Office of Fair Trading (OFT) has said.
Almost a half of those who did respond to a scam had lost more than £50, while 5% lost more than £5,000.
The OFT said 73% of adults had received a scam e-mail in the past year.
Some 6,500 people are also receiving letters from the authorities warning them that their names are on a "sucker list" being circulated by fraudsters.
The OFT is launching a "scamnesty", calling on consumers to drop scam mailings into designated boxes at public places or into an online "bin".
OFT chief executive John Fingleton said: "Scammers are using ever more sophisticated and cunning tactics to dupe people out of their cash.
"We want people to recognise the warning signs, and feel confident enough to seek advice from friends or family or from Consumer Direct."
Consumer Minister Kevin Brennan said the government had spent £7.5m to create "scambuster" teams across the UK.
"We are determined to fight these crooks," he said.
The National Fraud Authority has estimated the cost of fraud - including scams, online theft, insurance cheats and tax fraud - at £30bn year in the UK, the equivalent of £621 per adult.
The OFT is giving the following advice to help avoid being scammed:
Meanwhile, a list of 10,000 names - including thousands with addresses and telephone numbers - which was being shared by fraudsters has been seized by the City of London Police and the Financial Services Authority (FSA).
The two authorities have now written to 6,500 people on the list to warn them that they could be targeted by fraudsters looking to sell worthless shares.
These so-called "boiler room" scams have cost UK victims an estimated £200m a year. The 734 people who contacted the FSA last year to report becoming victims lost an average of £24,000 each.
"We are all potential victims for fraudsters and need to be aware of the heartless way they operate," said Det Chief Supt Steve Head, of the City of London Police.
Boiler room fraudsters usually contact people by telephone and use high-pressure sales tactics to con investors into buying non-tradable, overpriced or even non-existent shares.
The businesses running the scams are unauthorised, overseas-based, with bogus UK addresses and phone lines routed abroad. Dealing with an unauthorised firm means victims do not have access to financial complaints and compensation schemes.