The Internet also makes it easy for fraudsters to disguise or "spoof" their caller ID and make their pitch appear to be legitimate. They can use software that will display any name they want: your bank, local police department, even the FBI—and a bogus phone number—to hide their true identity and keep you from calling back.
"So, even if you think you know who's calling by checking the caller ID, you really don't," said Paula Selis, senior counsel with the Washington state attorney general's office. "You can no longer trust your caller ID. If you really want to do business with an entity that you know and trust, you have to call them."
Top telemarketing scams of 2013
Fraud.org analyzed all of the complaints it received last year and found that those involving a prize or sweepstakes topped the list, followed by phishing and fake check scams.
Prize/sweepstakes scams: They're easy to spot, although the pitch is often hard to resist. The caller says you've just won a big prize—a car, tropical vacation or a million bucks. All you need to do to claim your prize is to pay a fee. It could be a couple hundred dollars or a couple of thousand. You might be told the money is needed to cover shipping/handling or to pay for taxes. Whatever the reason, it's bogus. If you've truly won a prize, it's free—there's no payment required and you don't have to verify who you are by giving them your credit card number.
Phishing scams: The fraudster pretends to be calling from a company you do business with—usually your bank or credit card company—in order to steal personal information. They'll say there's a problem with your account and they just need to "verify" some information. They're trying to get you to give them your account number and PIN or password. Any company you do business with already has this sensitive information and they would never call to confirm it by phone or email.
Fake check scams: This con always involves a counterfeit check that looks real. The caller wants to buy something you've advertised for sale and they want to send you a check, typically for more than the amount of the transaction. They have all sorts of phony reasons why the check is for more than the selling price. You're supposed to deposit that check and wire back some money. Don't do it, even if the bank tells you the check has cleared. Once the bank determines that the check is a fake check, which can take weeks, that deposit will be removed from your account and you will be left holding the bag.
Recovery and refund scams: Telemarketing thieves know that if they can trick you once, they can probably fool you again to steal even more money. Some phone bandits work from lists of victims, what they call "sucker lists," to double-down on them. This time, they claim they can help you recover your lost money. They may say they're with the FBI or some other government agency. Of course, you need to pay them some money for this service. That's your tipoff to a rip-off. Hang up.
(Read more: Identity thieves gear up to steal your tax refund)
Scammers call millions of people each year who are on the federal Do Not Call Registry. Hey, they're crooks who are trying to steal your money or personal information; they don't care about some government phone list. If your number is on the Do Not Call Registry and you get a call from someone trying to sell you something, hang up and file a complaint with the Federal Trade Commission.
According to the National Consumers League, nearly a third of all telemarketing fraud victims are age 60 or older. Here is a tip sheet to help older Americans learn when to hang up.
—By CNBC contributor Herb Weisbaum. Follow him on Facebook and Twitter @TheConsumerman or visit The ConsumerMan website.