There is only one place in the Constitution where individual rights are granted together with an express caveat that they may be regulated: The Second Amendment (prior to DC v. Heller, it was unclear whether the Second Amendment granted individual rights at all).
The text of that amendment is as follows: A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
The other uses of the term (quoted at the end of this post) regard federal elections (art 1 sec 4), regulation of commerce (1:8), regulation of the value of currency (1:8), regulation of the military (1:8), regulation of commerce by the states (1:9), procedure in cases involving ambassadors (3:2), and control of federal property or territory (4:3) (4:2 was voided by the 13th Amendment).
The Founding Fathers surely did not throw the term "well regulated" into the Second Amendment as some kind of scrivener's error -- it must mean something. Perhaps it means the same thing it means everywhere else it appears in the Constitution: Congress is allowed to regulate the exercise of this right. Because whether it is a musket or a canon, it is deadly. As a practical political matter, they could not have meant to leave the right totally unfettered because surely slave states voting to ratify the Second Amendment weren't comfortable giving free African Americans in the north the right to stockpile munitions. I don't think that is a huge leap.
But there is a more fundamental issue at play -- one that actually harmonizes the "well regulated" language with the grant of a right: The 14th Amendment's Incorporation of the Bill of Rights. Until after the passage of the 14th Amendment, the Bill of Rights applied exclusively to the federal government. While the federal government could not, for example, pass a law requiring all children in public schools to wear crosses and be taught exclusively by priests, the state governments could. This all changed with a series of Supreme Court decisions that read the 14th Amendment as forbidding states from infringing rights in the Bill of Rights. McDonald v. Chicago includes an extensive discussion of the history of Incorporation, but does not address the characteristic of the Second Amendment: A specific reference to regulation.
Is it possible that the "well regulated" language was intended primarily to allow states to regulate firearms in order to make sure that a militia could be created or maintained effectively while preventing rogue militias from being formed? In the early days of the United States' republican form of government (small "r" republican -- states with broad rights, federal government with narrow rights), there was real concern about creating a strong federal government. It seems clear that the Second Amendment was adopted, at a minimum, to allow states to push back if the federal government behaved tyrannically and unlawfully.
Bottom line is that whether the "well regulated" language was intended to allow Congress to regulate or not, it pretty clearly was intended to allow the states to regulate firearms.
The Supreme Court has held that the Second Amendment creates an individual right to keep handguns regardless of federal law to the contrary (DC v. Heller), but by ignoring the context of the Second Amendment's creation, McDonald v. Chicago applies that right to the states in a way that (while perhaps the correct outcome with regard to handguns kept in the home) does not address whether the Incorporation Doctrine has in essence voided the "A well regulated militia, being necessary to the security of a free State" language. I don't think it has.
The United States has a long tradition of states having their own militias. These now take the form of the "National Guard". Does the Second Amendment permit the states to require that all adults without criminal records or mental illness own a firearm? Perhaps. Does the Second Amendment permit the states to limit firearms so as not to interfere with the security of a free state or with the security of its own militia? Probably.
Granted, these thoughts are more in the form of a thought exercise than an extensively researched paper, but I would love to hear a cogent answer to this question: "How can we discuss the constitutional limits to regulation of firearms without discussing the first three words in the Second Amendment: "A well regulated....".
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The term "regulate" or "regulation" appears in nine places in the Constitution. Only one of those uses (the Second Amendment) is a limited on the grant of a right to individuals.
Article 1, Section 4: The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Places of chusing Senators.
Article 1, Section 8: The Congress shall have Power To ... regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;....
To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;....
To make Rules for the Government and Regulation of the land and naval Forces;
Article 1, Section 9: No Preference shall be given by any Regulation of Commerce or Revenue to the Ports of one State over those of another; nor shall Vessels bound to, or from, one State, be obliged to enter, clear, or pay Duties in another.
Article 3, Section 2: In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
Article 4, Section 2 [voided by 13th Amendment]: No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due.
Article 4, Section 3: The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
Bill of Rights:
Amendment 2: A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
The term does not show up anywhere else in the Constitution, Bill of Rights, or other constitutional amendments.