The IRS never initiates taxpayer contact with a phone call or e-mail, but there are plenty of scammers posing as IRS agents who will. These folks are out to get you to give them enough personal data so that they can pose as you. Hang up from any phone calls from purported IRS agents, and delete any e-mail that purports to be from the IRS; do not respond to it or click any links. You can report the attempted scam to the Treasury Inspector General for Tax Administration (TIGTA) by calling them at 1-800-366-4484, or by filling out a form on the TIGTA website. Or you can just ignore it and do nothing. Read what the IRS says about tax scams: irs.gov: Tax Scams/Consumer Alerts.
These folks posing as IRS agents can sound very convincing. They may know personal information about you, sometimes even the last 4 digits of your social security number. Some phone callers are able to fake caller ID to make it look like the IRS is calling (e-mail scammers can also make it look like the IRS was the sender, although some don't even bother to try). They use phony names, and often make up fake IRS badge numbers. Scammers can be outright nasty, threatening you with legal action. Some will even go to the extreme of having another scammer call you, posing as the police or some other intimidating authority, such as the motor vehicle department.
If you think you're already a victim of identity theft, you should immediately head to the Federal Trade Commission's (FTC) website, IdentityTheft.gov. It has step-by-step information about what to do if you are a victim of identity theft. The FTC also produces a booklet called "Taking Charge: What to Do If Your Identity is Stolen," which you can obtain for free from Weinstein Associates. You can use this in conjunction with the information on IdentityTheft.gov. There are additional FTC resources and information available at the main FTC website.
The IRS has more information about tax scams and identity theft, including the following: