Yes, there is a taxpayer privilege. It is narrow, to be sure, but it exists. On July 22, 1998, President Clinton signed into law the Internal Revenue Service Restructuring and Reform Act of 1998. 
This amendment of the Internal Revenue Code, which included the so-called Taxpayer Bill of Rights, contained provisions intended to enhance taxpayers’ rights with the IRS. Included in this amendment was a limited evidentiary privilege that protects confidential communications between taxpayers and non-lawyer tax practitioners, including accountants. The amendment is codified at 26 U.S.C. § 7525.
For a detailed look at the taxpayers’ privilege, you should read Washington, D.C. lawyer Christine S. Hooks’ well written article, The Tax-Related Privilege You May Have Already Waived. Published in the March 2013 issue of The Federal Lawyer, and accessible here with permission, Ms. Hooks’ article explains the privilege’s relation to the attorney-client privilege and defines who qualifies as a tax practitioner for purposes of establishing the privilege. The article addresses the privilege’s scope and its exceptions. And, importantly, Ms. Hooks discusses how easily one can waive the privilege without careful attention to its application.
The article is a must-read for those dealing with tax-related communications, whether to an attorney or to a non-lawyer tax practitioner. My thanks to Ms. Hooks and the Federal Bar Association for permission to reprint the article in this post.