The United States Constitution does not explicity protect "the right to privacy" per se. There is no article or amendment that comes right out and says that. What the Constitution does protect is the right for citizens to speak their mind, to congregate peacefully in protest, and to be safe in one's home without unwarranted search and seizure. In addition, the Fourteenth Amendment builds upon the drafters of the Constitution's apparent intent by adding to the document the following language:
"All persons born or naturalized in the United States...are citizens of the United States...No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law..."
The phrase "life, liberty, or property" has been broadly interpreted by the courts to reinforce the framers' emphasis on a fundamental right to privacy. A link below ("law2.umkc...") will take the reader to recitation of this discussion along with links to the various court cases that have reaffirmed the right to privacy interpretation of the Constitution.
As a side note, the continued relevance of this discussion is increasingly apparent as the government and private citizens use modern technologies that can intercept electronic communications and provide video of spaces currently thought to be private, for example, aerial surveillance of one's fenced-in backyard could be considered an invasion of privacy. As unmanned drones become more prevalent, this discussion will assume greater importance.