Yes, if you collect any personally identifiable information via forms. Personal information might be as simple as a name and email or tracking information collected via analytics and used to measure aggregate site performance; it might be as complex and highly sensitive as social security numbers, credit cards, medical data or financial data.
A privacy statement or policy is one that tells your site users how you gather, use, disclose and manage any data you collect from them. But even if your site is nothing more than a static billboard and you don't collect any information via forms, it's still an important document. Today, many site users look for privacy information. People want to know if your site is using "cookies" or code to track them on or off the site. Privacy is a big issue and not getting any smaller.
Because there are legal implications to a privacy statement, you may want to enlist your attorney to draw up a policy. Or you may want to research and develop a draft and then run it by your attorney. What you need will depend on the type of data you collect and what you do with it. While there are no federal laws requiring you to post a privacy statement, there may be state-specific requirements or obligations in specific circumstances, such as the Health Insurance Portability and Accountability Act (HIPAA) and the Gramm-Leach-Bliley Act.