The Bill of Rights doesn't explicitly grant us this right, although, it doesn't deny it either. Government buildings have burned to the ground incidental to the protection of this right. Charles Dickens tells the story best here.
The word privacy appears to have first been used c.1450. The right to privacy has been discussed in legal(Harvard Law Review) circles as early as 1890. Legally, the right is no longer in force once we publish our data, or commit a crime--or seek to commit a crime, or breath oxygen. Abortion (National Review) runs rampant in this country today because somebody thought we ought to have privacy. Practically speaking, it is impossible, and imprudent to guarantee. New technologies today are both destroying it, and safeguarding it. Confidential information is sold, stolen, and lost. Lastly, you can try to get your cut of the action here.
Update: Oreilly warns us in the article below that our Privacy, is ultimately, in our own hands.