I agree with the above posters in that what we call Americans' "Right to privacy" is strongly suggested by the Constitution in the 1st, 4th and 14th Amendments, but it is never clearly or explicitly stated.
It was the court system in the United States, and especially the Supreme Court, that interpreted the Constitution in such a way that a reasonable expectation of privacy was the right of our citizenry. There have been literally thousands of cases where evidence obtained by illegal search was deemed inadmissible in court, upholding our right to both privacy and due process, unless the government can prove reasonable suspicion that a person has committed or is going to commit a crime.
The Supreme Court has ruled on numerous occasions upholding those same lower court rulings on evidence, then expanding privacy rights into both marriage and pregnancy, ruling first in Griswold vs. Connecticut that contraception and family planning were private matters, and could not be prohibited by the State, then in Roe vs. Wade that a woman had a right to medical privacy in making decisions about her own body with regards to abortion (though they did allow for second and third trimester restrictions to stand, thus offering only limited privacy rights).
So I would have to give the nod to the Judicial Branch for defining and expanding Americans' right to privacy.
I think that the expectation of privacy is something that was heavily implied in specific amendments in the Constitution. Its presence, while not explicitly stated, is felt at other points in the document. I am not sure we can openly state that there is a "right to privacy," the explicit wording not being present. Yet, the "look and feel" of privacy is undeniable. We can see it in some of the amendments to the Constitution. Part of the rationale behind the 3rd Amendment is the belief that a "man's home is his castle," and individuals should have the expectation of personal privacy to not house soldiers in their homes. This was in direct response to the British Quartering Act, which took away the private realm of Colonial subjects. Additionally, the Writs of Assistance, British measures which allowed for officers to search Colonial belongings without any probable cause, was another instance of Colonial privacy being vitiated. Its presence is felt in the 4th Amendment. The idea of personal privacy, a realm where individuals can be left alone to say and do what they feel so long as it does not impede on another's privacy, is felt in the 1st Amendment to the Constitution, as well.
The Right to Privacy, when discussed here in the U.S., usually means the right of citizens to be free from government interference in their lives. The Right to Privacy here in the U.S. can be originally found in the Constitution. Though the word “privacy” never appears in the Constitution, it is clearly implied. An excellent example, of course, is the 4th Amendment which keeps citizens and their property from being searched and seized without a warrant issued upon probable cause that evidence of a crime will be found. Another example is the 1st Amendment right to freedom of religion. Religion is a private matter and the 1st Amendment keeps government from interfering in the private lives of the people.
Of course, the Framers of the Constitution were very well read and many of these ideas concerning a Right to Privacy come from the ideas of Enlightenment thinkers such as John Locke and from older documents such as the Magna Carta and the English Bill of Rights, which limited the power of the government and gave more power to the people.