Answer:
It is controversial whether or not there is a constitutional right to privacy. Those who believe that there is no right to privacy reason that the right to privacy is not specifically mentioned in the Constitution. Those who believe that there is a right to privacy believe that a right to privacy is implied by the 1st, 3rd, 4th, 9th, and 14th Amendments.
One of the strongest arguments for the right to privacy is the events following America's independence. When the founding fathers discussed introducing the Bill of Rights, many were in opposition. The opposition reasoned that listing specific rights in the Constitution might imply that rights not listed therein are not rights of American citizens. Those favoring the Bill of Rights reasoned that if no rights are listed specifically, then no rights are protected. The Ninth Amendment was introduced to quell the fears of those against a Bill of Rights.
The Ninth Amendment of the US Constitution states, " The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people." This Amendment is used as an argument for the existence of a right to privacy. Those believing that a right to privacy does not exist often reason thus because the right is not enumerated. Those believing there is a right to privacy state the Ninth Amendment; a right not listed cannot be used to imply that it does not exist.
Another right that strongly implies a right to privacy is the Fourth Amendment. It states, "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." The only reason that a citizen of the United States would be opposed to unreasonable search and seizure is violation of privacy or because they are hiding evidence of a crime. This Amendment is reason for many to believe that the founding fathers had the right to privacy in mind while writing the Amendments.
The Fourteenth Amendment, in the last portion of the First Article 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; nor deny to any person within its jurisdiction the equal protection of the laws." Some might interpret the deprivation of privacy by the state as a violation of one's liberty. Further, prior to the Fourteenth Amendment, the Bill of Rights applied to the federal government of the United States alone. This Amendment bars state governments from violating the rights the federal government was barred from violating (i.e. Constitutional rights.)
The First and Third Amendments may also imply privacy. The first Amendment might be taken to imply a right to privacy of one's beliefs. The Third Amendment might be taken to imply a right to privacy within one's home from troops. Prior to the third Amendment, it was often customary for troops to quarter in the private residences of citizens. The third Amendment might be taken as evidence that the founding fathers had intended to imply rights to privacy.
Various non-Constitutional privacy laws have however been enacted, at both Federal and State levels. Examples of these include HIPAA (Health Insurance Portability and Accountability Act of 1996) which addresses medical patient privacy, the Privacy Act of 1974 (functionally a reinforcement and update to the IV amendment), and Gramm-Leach-Bliley Financial Services Modernization Act (financial privacy) among others.
Other areas where privacy laws have recently bloomed, predominantly at the State level, relate to medical issues beyond what is covered in HIPAA, including the special privacy requirements of AIDS/HIV patients and victims of criminal abuse.
Answer
While it's true the right to privacy isn't mentioned in the Constitution, the US Supreme Court decided privacy is an implied 1st, 3rd, 4th, 9th, and the 14th Amendment Due Process Clause.
The judicial concept is called "Substantive Due Process," which holds that the Fourteenth Amendment Due Process Clause is intended to protect all unenumerated rights considered fundamental and "implicit in the concept of ordered liberty," among these the right to privacy. Use of Substantive Due Process is considered judicial activism, in that it seeks to limit the scope of laws that undermine personal liberty, even if the law doesn't address a right specifically mentioned in the Constitution.
Earlier, Lochner-era (approximately 1897-1937, second industrial revolution) Courts used Substantive Due Process in a way that reduced protection of the individual against exploitation by businesses and the government, such as protecting the right of the individual to negotiate contracts with an employer by holding employment laws regulating minimum wage and work conditions unconstitutional.
Today, Substantive Due Process is used to protect the individual against exploitation or legislation that creates an undue burden on individuals, or on an identifiable group or class of citizens.
In order to determine whether the government has valid cause to interfere in people's lives, the Court applies a "rational basis test" to determine whether the legislation is related to a legitimate government interest. If the law passes the rational basis test, the Court next applies "strict scrutiny" to determine whether there is a compelling state interest that justifies violating the groups' or individuals' fundamental rights, and whether the law is applied as narrowly as possible to infringe those rights as little possible.