The conception of rights not specifically enumerated in the Constitution yet still being retained by the people is one that is supported by the 9th Amendment, though throughout the history of the Supreme Court, they have typically been overlooked by other means of achieving that very same result.The most famous invocation of the 9th Amendment comes from Justice Arthur Goldberg's concurrence in Griswold v Connecticut (1964), which upheld the right to marital privacy when seeking access to birth control. The Court agreed 7-2 that the right existed, though the real question was where exactly that right came from.

The plurality agreed with Justice Douglas, who argued that the 1st, 3rd, 4th, and 5th Amendments to the Constitution created a sort of "penumbra" over rights that are retained by the citizens. For example, if the Founders were so insistent that people have the freedom of association and speech, per the 1st Amendment, the right from soldiers quartering in the home (3rd), the right to be secure in one's possessions and property (4th), and the right to due process (5th), it makes sense that these rights extend over such rights as the right to make one's own medical choices and to enjoy the right to make decisions about one's body with the consult of one's doctor, and that the state's influence doesn't permeate those areas.

Justice Harlan wrote a concurrence agreeing that the right to access birth control existed, stating that the 14th Amendment's Due Process Clause (nobody may be deprived of life, liberty, or property without due process of law) was sufficient to cover the right to birth control, not the penumbra theory. The majority had shied away from this logic, as substantive due process was a constitutional theory that many of the justices (notably Douglas and Black), had been appointed to destroy. Substantive due process was typically used to protect a supposed "right to contract", in such decisions as Lochner v New York (1905) and Adkins v Children's Hospital (1923), which struck down a 60 hour work week and a minimum wage, respectively, as it infringed upon the liberty of individuals to enter into contract with their employer. As you can imagine, it didn't necessarily protect the rights of individuals as much as it allowed businesses to circumvent the legislative process to strike down labor laws that went against the laissez-faire policies of the day. The Court eventually rejected this "right to contract" in West Coast Hotel v Parrish (1937), or the "switch in time that saved nine" case, for those of you who remember that line from AP US History regarding the Roosevelt court packing plan. Essentially, Harlan was fine with using a line of doctrine that some of the other justices didn't want to bring up due to its negative connotations, and it being a less influential legal theory at the time.

Finally, answering your question, Justice Arthur Goldberg wrote a concurrence, saying that he would have decided that the 9th Amendment protects the right to access birth control, saying that the amendment grants substantive protections (i.e. the fact that other rights may be held by citizens implies that those rights exist, and that birth control is one of those rights that we have come to accept we have, and they may not be restricted by state action). Chief Justice Warren and Justice Brennan concurred with this opinion.

Since Griswold, the Court has become much more comfortable with substantive due process as a credible legal theory, and you can see it form the backbone of such rights as the right to an abortion per Planned Parenthood v Casey (1992) and the right to marry per Loving v Virginia (1967) and Obergefell v Hodges (2015).

In sum, the 9th Amendment was at one point a suggested means to prove that we have rights that exist beyond the scope of the Constitution's specific language, but it was proved obsolete by alternative theories of where we can find these rights.