In the US Constitution, the first section of the Fourteenth Amendment. The clause defines a US citizen as being anyone either born in the territorial borders of the US or having gone through the naturalization process, and states that such citizens have equal protection under the law.
The clause has had a few effects on US law. The biggest is incorporation - the forcing of the major parts of the Bill of Rights on state governments. The result is that if a state law is filed that violates the Constitution, it may be attacked as being unconstitutional, even though it is not a federal law. In addition, many civil rights laws rely on this as the constitutional framework on which they rest, as the law is a mechanism to protect the equal protection that the Constitution guarantees.
eliserh: While the Due Process Clause may be the technical point for incorporation, the equal protection clause is key as well, as it provides the rationale for incorporation (since all US citizens are given the same protections, those protections must be enforced equally.)