We received a very official looking letter from a company called iDNS (Internet Domain Name Service) notifying us that our domain was going to expire soon (it isn't) and that we needed to renew with them within the next 60 days (we don't). Scamming seems to have become somewhat of an established business model in the U.S., and it's becoming an increasingly frustrating cat-and-mouse game to try and keep from getting duped.
One good way to avoid these types of scams is not to do any sort of business that you didn't initiate. Don't click links in unsolicited emails, give out information over the phone, or anything of that nature. If you get an email from Google asking you to sign in to verify your information, instead go to Google.com and see if the request seems relevant. If a company calls you asking for personal information tell them you'll call them back, look up the phone number for the business online, and then call and ask them to provide details on the contact. It seems like a bit of a hassle but it doesn't come close to the amount of effort that has to go into cleaning up after someone gets access to one of your accounts.