The US has a wealth of state and federal laws intended to protect privacy, but what it doesn't have is a federal equivalent to the EU Data Protection Directive. There's even a law to protect privacy of video rental information (and if you're not familiar with the story behind that, then it makes for great reading). The US Constitution doesn't specifically protect privacy, although this is covered in the 9th amendment. Despite that, an aggressive Federal Trade Commission and active litigation combine to offer good privacy protection.
Security guru Bruce Schneier has called for a US privacy law - a federal equivalent to the EU Directive. I'm sceptical that this will happen, but it would certainly be worth a try.