Why did diffirent regions develop certain swords?

Why, for example, did the Arabic peoples create the scimitar, while the katana was developed in Japan, and the claymore came from Ireland? And the medieval Arthurian broadsword vs. the rapier? What made these people create the weapons they did? Granted, it would have been pretty weird if they all had made the same kind of pointy/sharp metal object, but is there a story behind the various types?

Just sort of making it up as I go along here, but . . .

Different soldiers in different places at different time had different needs? A group of cavalrymen would want a different weapon than a group of infantrymen, for example. The Samurai’s war was probably way different than that of the Roman Legionnaire or the Spanish Conquistador or the Viking raider. And different armies fought in different ways. And different groups had to overcome different kinds of enemies. Also, terrain probably figured in to things. And of course, technology. And, I would guess, economics (all them weapons were probably expensive). And then people started wearing armor and changing their weapons up so other people changed their weapons and armor up and so forth, and it all took different paths in different places . . .

I’m sure someone will be along with a better ordered description of the evolution of swords soon.

Well, not sure if this will address the whole of your questions, but I was watching modern marvels last night, and it happened to be about swords. Basically different typse of swords were developed for different purposes and against differring armor. You had your sharp edged swords with thicker blades to slice, different swords to thrust. The balance of weight within the sword would be used differently. If you compare a broad sword with say a fencing sword, these are made for two completely different uses and situations. These depended on what type of armor your enemy would be wearing and how they would typically be armed. This was however limited to Europe, but I imagine these circumstances would have played a role. Also, one has to look at the swordmakers and smiths, maybe they made advancements in technology that would enable them to make a lighter, sharper blade and these technologies or techniques were picked up faster in some places than others. Also, the average physical condition of the people employing these sword can be taken into consideration, whereas big heavy swords would not be as useful where the people are smaller and nimbler.

a little more, take the scimitar for example, usually in this region you did not have people wearing armor, so this type of blade was an effective weapon for slicing you opponent, whereas in regions where armour was used, and especially later where it was plate armour, these swords would have littel to no value, you needed something to penetrate, a straight, skinnier thrusting sword. Axes or spears were more popular in this case as well.
Here is a graph showing the evolution of swords:

The general answer encompassing all the correct responses preceding is that swords evolve for specific tactics (and changes in sword design usually reflect attempts to modify tactics in the ongoing arms races).

For example, soldiers fighting in formation (classically, the Roman infantry) cannot wave about great long swords that will get in front of the strokes of their comrades, so the Roman short sword was actually less that two feet long, allowing the Romans to fight shoulder to shoulder so that the enemy could not get behind them. The Celts that the Romans faced fought in loose formations and used longer swords to allow each man to defend himself in individual combat.

Cavalry swords are nearly always curved because a straight sword is more likely to “hang up” if one is slashing at an opponent as one rides by. (The apparent contradiction would be the long swords of the European knights, but their mounted weapon was actually the lance, with the sword being more often used once they dismounted or were unhorsed.)

Rapiers are a dueling weapon that allow an unarmored fighter to keep their opponent at a distance. (As with the Celtic mode of combat.)

Beyond that, once a particular style developed, any successor swords would tend to follow the tradition originally set by the earliest sword, so the Japanese katana (which had a cavalry sword as an ancient ancestor) maintains a slight curve, while the rapier (descended from the long sword) is straight.

In addition, various developments in metallurgy or different developments in armor also affected the ways in which swords developed. (E.g., a katana made of stiff iron would be too heavy and too brittle to be effective.)

Different Cultures, Different Swords: Why?

Pretty much everything said is on the beam.

Add also that the availablity and quality of metal, and knowledge of alloys is a huge factor. If a culture grows up in an area with weak metals and/or a poor knowledge of refining, swords are more liable to be thick and heavy, just to avoid breaking.

But there’s also a less rational factor. Ancient people (prior to 1950 that is) developed by trial-and-error, and by superstition. There were no scientific methods to test the strength, resilience or shape of a sword. We’re not talking about protracted experimental research projects here, but “making swords the way great-granddaddy used to do”.

If I recall correctly, for example, the channel that’s cut in the side of blades to “let the blood run out” is completely useless. The weapons with cute hooks at the end, or serpentine blades must be mostly show pieces. Having fenced for several years, there are quite a few weapons that look like “instant losers” against a straight, top-quality saber or epee. That’s regardless of whether on horse, fighting against a shield, or an armored knight.