Counterfeiting is a billion, if not trillion dollar activity. It is very often a factor in any clandestine or crime operation. First place to learn about money, counterfeiting and anything related to financial crimes is the Department of US Treasury web site and more specially to identifying real versus counterfeit money is the USSS Know Your Money page.

An entire federal US crimes division called the Financial Crimes Enforcement Office has a number of articles and information. The "Money Factory", or the Bureau of Engraving & Printing has a lot of information about cash & paper money and a page with their counterfeit laws.

The Office of the Comptroller of the Currency, Administrator of National Banks exist to ensure a safe and secure national banking system in America. This branch is also under the US Treasury department. 

Finally, one of the more fun and informative government sites about counterfeiting is the Bureau of Engraving and Printing's Get Real or Get Even web site.