The 2nd Amendment to the US Constitution says:
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
There is no consensus in the US as to what that really means these days.
When the Constitution was written, the ability of the citizens (meaning white male land-owners) to possess arms was considered necessary not only because the US was still largely a frontier nation with no 911 service, but also because an armed citizenry was less easily suppressed and controllled by a potentially corrupt or unjust government.
However, back then, the citizens had the practical ability to possess the same level of firearms as the government. These days with tanks, missles, aircraft, smart bombs, nukes, bio-chem, satellites, etc, it's unlikely that a bunch of dudes with pistols and shotguns are going to be able to prevent the government from oppressing them if it decides to.
The range of public opinion spans all the way from people that think no private citizen should legally be allowed to possess any kind of gun to people that are grumpy that they're not allowed to buy 2 or 3 cases of the newest machine guns and hand grenades and would drive an M1A1 to work if there was parking available.
Generally, it's legal for any citizen to own a hand gun, shotgun or rifle. States have various laws regulating WHO can own a gun (convicted felons usually can't, for example) and what KINDS of guns are legal (fully automatic guns, assault rifles, certain types of ammo, laser sights and noisy crickets are illegal in many states, etc).
So the simple answer to your question is that US citizens are allowed to own guns in every state. Who and what kind of gun varies, though.
FYI, the conflict between state laws and the US Constitution has been going on since 1787. On paper, the US Constitution is the supreme law of the land and no state law can override it. The practice of determining what state laws are unconstitutional is very complicated and promises lasting job security for hordes of lawyers.
Hope this helps.
** Political sig removed **