Internally, the gun laws can vary within any given state. (Talking about the US here.)
Pennsylvania has a set of state level requirements regarding ownership and carry. It's a "Shall Issue" state where if you apply for a permit to carry, the state must have a reason to deny you such as a record felony, domestic abuse, involuntary mental institutionalization or something that the Sheriff could take to court to say he had solid cause to think a person was a danger, such as a guy screaming into his cell phone that "I'm getting my permit right now, then I'm gonna get a gun and come shoot your cheatin' ass." There's a mandatory background check for firearm purchases, but no waiting period other than how long it takes for the instant check. The fee is about $15, just enough to defray the costs of the paperwork.
Pennsylvania's state constitution has a supremacy clause which prohibits local jurisdictions from enacting restrictions on gun ownership and carry which would superscede or contradict the established State laws. That means Philadelphia or Pittsburgh can't enact a waiting period or ban on ownership, purchasing or carry, nor could they go the other way and declare that no permit was required for concealed carry. So a permit to carry is good anywhere in PA outside a business where the owner says "no guns in my place" or various government buildings, schools, and the like. As a result, you know where you stand as far as the law goes when you're in the anywhere in PA.
California, on the other hand, allows municipalities to enact their own laws, so long as they are not less strict than the state standards. So you could be in one county where it's legal to carry with a permit, and drive through a town where you're breaking the law the moment you pass through the corner of it's jurisdiction. To carry or even transport firearms safely and legally in that state, you must literally research the laws of every county, city, town or borough which you expect to travel through. So if your characters are traveling in one of these states, your GM has a golden opportunity to hand you a real Bag of Dicks if he's that sort of nasty minded GM that's always the most fun to game with.
Many states have reciprocity agreements with other states that hold the same standards for a permit to carry. 15 or so states will honor my Pennsylvania permit, no questions asked. But driving thought the states between those states could be a problem. In some states, you might be fine simply unloading and securing the weapon in a locked box in your trunk with the ammo stored separately... but in others like Maryland, even that would be No Go. Monster hunting roadtrip a la Supernatural? See above, Bag of Dicks if your GM is so inclined.
GM's can also use (and gleefully abuse) the fact that the Law isn't always what happens when the police are involved. One cop might ignore the sawed off (Federal felony) shotgun behind the bar in Old Lady Johnson's house so long as the owners keep their nose clean. And another cop might decide to be a Plot Complication even though the player characters might be toeing the line of the law in the instance.
As has been noted earlier in this thread, what's legal and what this or that police officer thinks is legal aren't always the same thing. I was jacked up for Walking While Goth during the post-Columbine 20-20 fueled fear mongering about "the Gothic movement, violent and black!" and the "dangerous Goth Gangs..." and I was given the third degree about why I was carrying. I replied politely that I have the required permit. The policeman claimed it wasn't valid in Pittsburgh, and I responded politely that the commonwealth's constitution forbade local bans. I didn't mouth off or give him attitude, but I made it plain I was aware of the law and my rights in the state. He wasn't happy about it and said so... but he didn't have much choice unless he wanted to try to fabricate a crime right there.
Now, on the flip side, almost every other cop I've talked to were fine, once they saw my permit. I've had a few particularly sharp officers spot that I was carrying (holster lines, don't you know) and inquire if I had a permit. I'm sure they were eyeballing my attitude and demeanor as much as the permit (is he sweating, stammering, otherwise worried about our interest?). And these encounters always ended amicably, usually with both parties scribbling down the address of a good range or shop with good prices. So, GM's, apply the Gamer version of the Skippy test and ask yourselves "do either of these scenarios bring to mind plot complications that make me giggle for more than 8 seconds? And will it make my Players cry for more than 8 minutes?"
So if a Storyteller wants to use gun laws as an opportunity for complications, or an opportunity for his characters... and villains... to gear up, it's easy to check a given state or country's gun laws. Wikipedia can give you general info most any country and state. For those setting games in the US, you can check out the NRA's website. Like the Open Carry site, it is a site belonging to a sociopolitical faction pushing it's own agenda (and we'll not discuss that agenda here)... but it does have a convenient map where you can check the specifics of any state's gun laws. So your Chicago based characters can run into a whole world of complications and gun culture shock if they head to Dallas Texas or Allentown, PA, and vice-versa.
And remember, a gun permit won't generally let you carry a concealed sword, axe or mace. That Warden's sword could land 'em in a heap of trouble even if the players have a "concealed weapons permit."