The U.S. Supreme Court heard Griswold v. Connecticut in 1965, probably one of the most important cases leading up to Roe v. Wade. The law at stake was a Connecticut ban of the sale of contraceptives.
The state's arguments for the contraceptive ban are interesting. There are two justifications. One is a consequentialist argument based on the assumption that it's bad for there to be population decline, which required looking at the 1960 census and seeing the population diminish from 1950 to 1960. (The population loss actually tells you nothing if you can't show that the population loss is based on birth and death rates, because it ignores the possibility that people moving from one state to another cause the biggest portion of the change, as the opposing lawyer pointed out.) In any case, the idea is that population decline is a bad thing, and it's therefore a good thing to pass laws preventing people from contributing to that by choosing to have sex without having children.
The second argument given by Connecticut is aimed at preventing immorality, but the immorality in question is not the immorality of contraception (which would have been more controversial) but the immorality of adultery. How does banning contraception diminish the likelihood of adultery? People are less likely to have adulterous relations if they think it might give rise to children.
The second argument is pretty poor. The first might have some basis if the population decline is so much as to be truly harmful to some important good, but that surely was not the case with Connecticut in the early 1960s.
So I don't think there are very good reasons for the law. But I was completely unconvinced of any constitutional argument against the law. Interestingly, the lawyer opposing the law was adamant that he didn't think taking his side would mean prohibiting abortion bans, which the Supreme Court went on to do within a decade, using this case to justify the right to privacy that they found in the Constitution in this case (a basis Ruth Bader Ginsburg repudiated in her Supreme Court nomination hearings almost thirty years later, despite her support for abortion rights).
I wonder if we'll see the same exact phenomenon with Lawrence v. Texas and same-sex marriage. Lawrence declared bans on same-sex sexual acts to be unconstitutional by a 6-3 vote. In the opinion, Justice Kennedy took great care to insist that their decision did not require a constitutional right to same-sex marriage. If the Supreme Court does declare bans on same-sex marriage to be unconstitutional, will they cite Lawrence v. Texas as precedent for the principles they use? There's certainly precedent for using cases that say they don't imply something to argue that they do imply it.