Actually Roe vs Wade implied the right to privacy from the 14th amendment:

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.

The alternative "right to privacy" has been found by other cases in the generic 9th amendment:

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

The (generally accepted) argument is that it's implicit in a number of the amendments that make up the Bill of Rights. It's not explicit however as Robert Bork argued during his SCOTUS confirmation hearings to his detriment. I think Griswold v. Connecticut is still considered the primary ruling on the matter.