That's a very broad question, covering many centuries and hundreds of miles across, but I can give you some information on Medieval England, at least.

The Calendar of Letter-Books of the City of London, A and B, between them covering from 1275-1312, detail a number of arrests in which carrying weapons is specifically cited as part of a charge, or a charge itself:

*"Writ of King Edward I. to the Mayor and Sheriffs of London enjoining them to punish all bakers, brewers, and other misdoers walking the City by night with swords and bucklers and assaulting those they met..." This seems to indicate that while carrying a sword and buckler isn't itself necessarily a crime, it is a crime to do so at night while carrying out another crime, a bit reminiscent of current laws in the USA about possession of a firearm while committing or attempting to commit a felony, whether or not the firearm was specifically involved.

• [A very long list of names followed by] "arrested for divers trespasses, homicides, robberies, and assaults, and for being nightwalkers after curfew in the City with swords and bucklers, and for setting up games near the City, contrary to the King's peace and the ordinance and statutes of the City of London..." wherein being out at night (past curfew) with weapons is itself a charge, though as it's lumped in with many more it doesn't indicate if that itself would have been worthy of arrest, had they not been charged with a litany of other crimes as well.

• [Again, list of names followed by] "are night-walkers with swords and bucklers, contrary to the peace, &c., and statutes, &c. Let them therefore be kept in safe custody..." In this case, being out at night with weapons does alone seem to have warranted arrest.

• "These are the articles which our lord the King commands to be kept in his City of London for the preservation of his peace. Firstly, that whereas murders, robberies, and homicides have in times past been committed in the City by night and day, it is forbidden that any one walk the streets after curfew tolled at St. Martin le Grand (fn. 3) with sword, buckler, or other arm unless he be a great lord, or other respectable person of note, or their acknowledged retainer, bearing a light; and if any be found doing the contrary they are to be committed to the Tun, and the next day brought before the Warden or Mayor and Aldermen, and punished accordingly. No taverner to keep his tavern open for wine or beer after curfew, nor admit any one into his tavern nor into his house, unless he be willing to answer for the King's peace, under penalties named... No one to keep a fencing school by night or day, under pain of imprisonment for forty days." Here it is stated that certain *wealthy and important) individuals may carry weapons, even at night, provided they have a lantern and aren't sneaking around: it also forbids fencing schools.

Moving a bit later to the later Calendar of Letter-Books of the City of London, H and I looking into the late 14th/early 15th century, notably well into the 100 Years War, there seems to be some specifications related to that state of war and a little more explicit exemptions.

• After describing the call to service for all eligible men, consequences for what is essentially draft-dodging, and banning price-gouging... "that no foreigner of any nation whatsoever carry knife, baselard, sword, or any arms, and that no one wander about the City after 9 o'clock."

• Very shortly after, a clarifier is made, "Ordinance forbidding any stranger or foreigner to carry sword, baselard, dagger, "hache," or other arm, unless he be an esquire of a lord or a knight's valet, who may carry his lord's or master's sword in their presence" which, similarly to above, seems to give a high-status exemption.

• Again, this is seen with "it was King Henry's wish that his lords and other of his lieges from divers parts of the realm should come and reside in London during the Emperor's stay, the Sheriffs should make public proclamation restricting the carrying of swords or other weapons in the City to knights and esquires under penalty of forfeiture" -- A wealth and status exemption.

Edit: correcting provided volumes of the document

As another user mentioned this question is quite broad but I can add a little flavor from my own focus of study (Japan).

There was nothing to my knowledge that went as far as to have registration of swords, but the regulation of weapons has appeared regularly in Japanese history.

Of course you have examples very similar to other areas of the world, making it illegal to wear swords or weapons in the presence of certain high ranking officials or the emperor and the like. The use of swords to denote rank in Japan (as only a samurai was allowed to carry two swords during later periods) ended up acting as a sort of weapon control that was really more of a delineation of class than anything else. Of course you also have the famous example of the introduction of the tea ceremony into polite society in Japan required it’s own forms of weapon policing, and entryways to traditional tea rooms are actually designed to keep someone carrying weapons from entering easily because of their small size.

There have actually been a number of sword hunts conducted in Japan—basically the search for and seizure of swords from private citizens. The most famous is one conducted by the Warlord Toyotomi Hideyoshi, but I’m not as much of an expert on this one, so I will leave it up to some of the Sengoku experts in the subreddit to take care of. The sword hunt I am most familiar with is the one that took place during the Meiji era which was one part in the abolition of the social caste system and also getting weapons out of the hands of possible upstarts. Weapon ownership laws from this period are actually still around and form some of the basis of private firearm possession law here in Japan.

One slightly off topic point you might find interesting is that in addition to weapon controls Japan actually instituted strict regulations on defensive structures during the Edo period. With a couple of exceptions that Tokigawa shogunate limited feudal domains to a single castle to reduce the defensive ability of possible insurrections.