The second amendment to the US Constitution states:
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.
What, if anything, about the law(s) in the US would be different if the italicized text had been omitted?
The operative clause is constrained to interpretations that are consistent with the prefatory clause. "But apart from that clarifying function, a prefatory clause does not limit or expand the scope of the operative clause." DC v Heller 554 U.S. 570 (2008)
The majority in Heller, after interpreting the operative clause "return[ed] to the prefatory clause to ensure that [their] reading of the operative clause is consistent with the announced purpose."
In their case, since their interpretation of the operative clause was consistent with the announced purpose in the prefatory clause, the prefatory clause may seem to have no effect.
However, they make the point that other interpretations of the operative clause can be ruled out by cross-checking against the announced purpose from the prefatory clause: "petitioners’ interpretation does not even achieve the narrower purpose that prompted codification of the right."
The court writes that if the petitioners had their way, only state-organized militias would be the beneficiary of the 2nd Amendment protections. However, the majority does not read the prefatory clause this narrowly. "[If] the organized militia is the sole institutional beneficiary of the Second Amendment’s guarantee — it does not assure the existence of a “citizens’ militia” as a safeguard against tyranny." The majority reads the prefatory clause to refer to a "citizens' militia": "the Militia comprised all males physically capable of acting in concert for the common defense".
The preface has colored the application of the amendment. For example, without the preface it is hard to imagine something like the National Firearms Act of 1934 (NFA) being upheld as constitutional. The NFA was upheld by SCOTUS in United States v. Miller specifically on the opinion that the Second Amendment does not protect a citizen's right to weapons lacking "any reasonable relation to the preservation or efficiency of a well regulated militia."
(The fact that all NFA-regulated firearms have, since that decision, come into common military and police use may leave one wondering how SCOTUS would address a Second-Amendment challenge of the NFA today.)
Absent the italicized text, it is possible that some government would have tried to pass a law prohibiting any group of people from gathering, training, and generally forming themselves into a well-regulated militia. The absence of such laws would thus be an answer to the question.
Militia-dissolving/preventing laws like that might have been not covered by the First Amendment "right of the people peaceably to assemble" nor the Second Amendment "right of the people to keep and bear Arms," without the italicized text clarifying intent.
However, even with the italicized text in the constitution*, the government(s, at various levels) gain a lot of power to disband groups of people who are trying to organize that way, by classifying them as terrorist groups, even before such groups have killed. So, it's not clear how strong the possible effect on laws identified in this answer actually is.
(*): Not differentially italicized there, just in this Q&A for ease of reference.
