When the Bill of Rights was adopted in 1791, it was seen as a set of restrictions upon the federal government, not upon the states. It wasn't until after the Civil War and the enactment of the 14th Amendment that the BoR was seen as applying to the states.
What throws a wrench into the mix is the doctrine of "incorporation" which was adopted by the Supreme Court, the highest court in the country. Essentially, this means that until the court "incorporates" a particular amendment in the BoR against the states in a decision, the states can take the position that it does not apply to them.
With respect to the meaning of the Second Amendment, it refers to "the people," which is a term of art used in several places in the Constitution and BoR. In ruling on other parts of the BoR, the Supreme Court has always held that "the people" refers to individuals, not some collective. The court has even referred to the Second Amendment as an individual right in passing, in cases regarding other parts of the Constitution. E.g., US vs. Verdugo-Urquidez (1990).
Yesterday, the Supreme Court granted certiorari to hear the Heller case, which challenged the District of Columbia's handgun ban on Second Amendment grounds. D.C. was a good venue for asserting the Second Amendment because it is a Federal territory, not state, so whether the Second Amendment is incorporated against the states is irrelevant.
What makes Heller so important is that it's the first time in 70 years that the court will be directly addressing the Second Amendment and whether it's a fundamental, individual right. "Fundamental right" is another legal term of art, and if the court does hold that the Second is one, then it will incorporate it against the states.
OK, so what about state constitutional provisions on the right to keep and bear arms?
The wording of state RKBA provisions varies quite a bit by state. 43 of 50 states do have such provisions, however. Some of those provisions are weak, e.g., Illinois's provision subordinates the RKBA to the police power, effectively rendering it moot.
In contrast, other states have very strong RKBA provisions, e.g., Pennsylvania. Pennsyvlania's constitional provision reads, "The right of the people to keep and bear arms in defense of themselves and the state shall not be questioned." (Pa. Const. Article I, Section 21.) It has been recognized by the state supreme court -- the final arbiter of what PA state laws mean -- as an individual right.
There is a list of every state's RKBA provision located at RKBA.org.