In certain kinds of stories, you want characters to have weapons. It's important: They need weapons to fight, their choice of weapon may reflect their personality, and it makes them look cooler.
The problem comes when you give The Hero a rapier, The Lancer a scimitar and The Big Guy a broadsword.
In real history, the development of swords in particular meant that each kind of sword had different uses. Broadswords, falchions and katanas, for instance, were designed for infantry to deal with their creators' versions of heavily armored opponents. Scimitars, cutlasses and sabers were for cavalry to cut down unarmored infantry. Rapiers, epees, small swords and the like became popular as both civilian self-defense and dueling weapons, and were rarely seen on the battlefield. Firearms and armor co-existed for a while (approximately three centuries), but eventually firearms made metal armor obsolete until the first practical bulletproof vests were created in the early 20th century.
In fiction, however, that goes right out the window. Scimitars and sabers will be used by unmounted people against straight swords, and it's almost a given that both combatants will be unarmored. A character in battle with a heavily armored combatant won't use a mace to smash in the armor and pulp the guy inside or even use a straight sword to stab him between armor plates; the fighter without armor will probably dispatch the armored fighter in a more exciting way. And of course, a Medieval European Fantasy might have the odd Katana show up in the hands of a really cool Bad Ass.
A kind of Anachronism Stew. Justified by Rule of Cool. Some may try to Hand Wave it by having the weapons be more representative of a culture or nation rather than personality type, despite the clear impracticality of such a thing. Not to be confused with Swiss-Army Weapon, which includes everything but the kitchen sink.
One Piece: Many organizations, even armies, don't have a proper, "uniform" equipment. Among the egyptian-like members of the Alabasta army you can see polearms, katanas, zweihanders, morning stars and muskets.
Actually, that example is an aversion. The organized Royal Army actually does have uniform equipment. The Rebel Army is justified in adhering to this trope, as they were specifically stated to have scrounged up weapons from wherever they could get them.
Invoked by the Muhou Ryu members in Gamaran: While all the other ryuu (schools of martial arts) are focused around one type of weapon, the Muhou Ryu includes many types of different fighting styles, hence different types of weapons, ranging from katana to spears to rapiers and weird swords to western halbeards. A notable example is given by the 47th Division: Their leader wields a huge spiked club, while the members wield lots of weapons including huge swords, hammers, polearms and gauntlets.
The Matrix Reloaded, when Neo fought The Merovingian's agents. Considering that everyone literally grabbed weapons off the wall, and that they were fighting in the Matrix, it makes sense.
And there might have been a hole in his defense - using every available type of attack made sense.
Redwall: Where do we start? Everything from rapiers to tree-trunks, slings to ballistas, cutlasses to teeth-and-claws makes an appearance. And of course, the hero gets the blade of Martin the Warrior, a straight bladed double-edged sword in accordance with the usual rules. Everyone else gets whatever their species usually uses.
Justified in The Baroque Cycle. A very wide range of weapons come into the hands of various characters throughout the story, but everyone has a very specific reason to be carrying that type of weapon. When weapons are used, their appropriateness to the situation is almost always examined in detail. No one can ever accuse Neal Stephenson of not showing his work.
In the Hawk & Fisher series, Hawk uses an ax instead of the standard-issue police sword. Justified because he'd lost an eye and lacks the depth perception for refined swordplay.
In The Lord of the Rings each member of the Fellowship has slightly different weapons; justified by the fact that they come from different cultures and backgrounds (and have very different heights). Legolas, has a bow and a long knife, Boromir uses a sword+shield, Aragon uses a Bow and long sword, the Hobbits also have long double-bladed knifes, Gimli has a few different axes, and Gandalf uses a staff and/or long sword.
The tabletop RPGDungeons & Dragons is one of the biggest offenders in this particular category. Many worlds have lightly-armored characters wielding rapiers and scimitars alongside heavily armored guys with big whacking great swords and great axes. But then again, D&D's armor system makes heavily-armored fighters harder to hit rather than reducing damage (something that you can also do with light armor and a high enough Dexterity score), and the threat range on scimitars and rapiers make it easier to score a critical hit. The first edition rules did have "weapons effective against armor type" charts, but this was phased out in second and subsequent editions. As this editor recalls, chopstick vs platemail was a -10 modifier.
When it's relevant to note that a blow simply made contact that was/might have been blunted by armor, 3rd Edition made use of the "touch AC" stat. It was mostly used for certain spells or attacks that involve grabbing the target rather than striking it.
This is also noticeable with canon characters in the various game worlds. For example, in the Forgotten Realms, Drizzt Do'Urden fights with twoscimitars. Artemis Entreri fought, for a long time, with a saber and dagger (he eventually got a straight-bladed sword that was more heavily enchanted). And so on.
In their defense, the oddness of these choices was noted. A lot of Drow are ambidextrous and Drizzt is supposed to be an epitome of this. Entreri was, through extensive training, just about on par with Drizzt, and at least he was wielding a light weapon in his off-hand.
That's because everybody believes that long swords were used with one hand. Every long sword was used as a sword to one and a half hands, meaning there are moves where its used with one hands, but just as many with two hands, and every rest position uses two. The short swords that were used with only one hand are basically long knives. The same goes for other weapons except rapiers and such, because these are so thin, that they are light enough. A one handed axe is called a hatchet, an "normal" axe is a two handed weapon.
Most fantasy games feature this due to their D&D ancestry. Palladium Fantasy. Warhammer Fantasy Role-Play, Anima, and the Riddle of Steel all follow this trope.
Certain modern era action games and cyberpunk games will feature a more modernized version of this, where anachronistic melee weapons, small personal defense firearms, and military hardware suited to bringing down a corrupt third world regime will all be given equal time and consideration on the weapons list.
GURPS: Dungeon Fantasy doesn't even bother with pretending that this doesn't happen, players are given access to all weapons from TL 0 to 4 because that's how the genre works. Also flamethrowers...
Slightly deconstructed by the fact that GURPS uses reasonably realistic stats for all weapons - thus, using a weapon wrongly or against the wrong opponent will make the fight harder for you. The character templates and loadouts often try to match a fighting style (I.e. your choice of combat skills) with the appropriate weapon.
Eon has everything from humungous two-handed swords, all the way down to thin little rapiers. Granted, you rarely see them in the same geographical area; you're more probable to encounter light weapons where people don't wear as much armour, such as on the high seas, or with isolated cultures that haven't had the need to develop heavier weaponry. When it comes to the players themselves, the unforgiving and detailed combat system keeps them in check, with light weapons being almost completely forsaken in place of spears (!) or broadswords, as any hostile encounter is a potential death-trap if you're not completely sure of what you're doing, and heavier equipment helps even the score.
The Elder Scrolls games include Katanas, wakizashi, tantos and Orcish Samurai armor along with early Medieval armor, claymores, longswords and sabres. Rapiers are absent however. According to the backstory, what we would call the Asian weaponry — tantos, wakizashis, katanas, and dai-katanas — are from the Akavir continent and exclusive to the Tsaesci (one of the four races of Akaviri known). The explanation of the Samurai suits is trickier: the Orc country Orsinium was allowed to exist during the rule of an Akaviri Potentate which may indicate inspiration. Blades armor and weaponry are based on Akaviri designs. The armor resembles Roman Lorica Segmentata, while the swords consist of Katanas.
More recent games have phased this out a bit - after Morrowind, you'll only see katanas with the Blades (and no other Asian weaponry anywhere), and the Orcs wear armour that has more of a Mongolian look.
Warcraft, especially World of Warcraft, is pretty guilty of this. For the most part, it doesn't even really matter which kind of weapon you are using, although a few classes can specialize in weapon types (and Rogues need daggers for Back Stab moves). But there is no inherent difference between an axe and a sword, other than the fact that not all classes can use both.
Most games in the Final Fantasy series basically select weaponry choices based on personality or an abstract battlefield role within their battle system, at best simplifying the attributes of a particular weapon style to fit. Somewhat averted in Final Fantasy X, which generally takes into account the need for different kinds of weapons for different kinds of enemies, but in a pinch, anything will usually work, just not as well.
Gameplay and Story Segregation occurs in that respect in an unusual way in Final Fantasy X. The plot implies that Wakka's Blitzball, a thrown weapon, is best for use against aerial targets. In actuality, Wakka just starts with higher accuracy; ANY character with the same accuracy (and luck) stat would have the same chance of hitting a given target, whether they're using a blitzball, a sword, or even a doll. This is also the case for Auron's swords and armored enemies- His swords almost always have piercing by default, but once you get to item crafting, the piercing attribute can be given to anything. In a nutshell, you could theorically run any character through another character's path in the Sphere Grid and have them behave exactly the same, except for Overdrives.
Zig Zagged later- when fighting distant enemies/objects, Waka is the ONLY melee character capable of hitting them, and your only other option is magic.
Dynasty Warriors and Samurai Warriors brings new meaning to the Kitchen Sink part of this. It has a ridiculous number of weapons that have no right coexisting the way they do, varying from the improbable (flutes, fans, and children's toys), to ones that shouldn't be present given the setting (boomerangs), to the misused (chakrams being used primarily as melee weapons; Chinese dagger-axes being dual-wielded or thrown). But it's cool, so who cares?
To prevent misunderstanding, they aren't chakrams, it's misnamed. They are fire and wind rings, large balded rings designed for melee and NOT meant to be thrown, their increased size is what makes the main difference. Another habit of the games is to name some weapons inaccurately, but using the name most people would call the weapon, such as calling seals made for magic focus a cursed deck, or the above mix up with the rings. Sometimes it's easier to spot than at other times.
Lloyd: I thought if one sword had an attack of 100 then two swords would have an attack of 200 right?
In Phantom Brave, anything you can pick up can be used as a weapon, from sunflowers to starfish to werewolves. ...And then fused with everything else to combine skills, so you can end up with a sword that slaps like a fish or a pumpkin that stabs like a spear.
Wanna play some Samurai Shodown? Then get ready to watch the Lady of War use her rapier to parry a huge stone pillar. Or perhaps you'd like to watch Andrew Jackson block a shot from a sledgehammer with his rifle? Or maybe a Cat Girl using a boomerang to block a polearm is more your flavour.
The Soul Series features a number of characters from different cultures of the 16th Century, and all fighting with different historical weapons and even a few fictional ones.
Fire Emblem: These games go back and forth on this one. The trope is played straight in the notion that there are many, many kinds of weapons from swords, axes, lances and bows, many of which are nonsensical (one of Eliwood's better weapons throughout FE 7 is a rapier that does bonus damage against calvary and heavily armored units). This trope is subverted in the sense that most weapons have a bonus for attacking a certain type of unit or a certain weapon style in a weapon triangle.
Unwritten Legends is a particularly egregious example, in that just about every pre-internal-primer cartridge weapon you can think of probably has at least one example in game.
Dragon Age: Origins, apart from the elvish curved blades most every sword or dagger is a medieval European straight blade, and if you are going to be fighting heavily armored foes you probably are going to be using a mace or warhammer.
The warhammers are ridiculusly wrong, real warhammers looked like slightly bigger claw hammers. Also, Maces were ineffective against plate, they were just more professional clubs.
Team Fortress 2 originally mostly used unique variations of Standard FPS Guns and this trope only applied to the melee weapons, which included things from knives to bottles to bats to bare fists. The unlockable items have since plunged headlong into this trope, with things like bows, crossbows, cans of soda, sandviches, flags carried around with a bugle, shields, boots, tranquilizer guns, flare guns, remote controls, lasers scavenged from crashed alien delivery ships, and jars of piss.
In Rune Factory 3, various townsfolk who accompany you to battle will carry a cutlass, a katana, a double-headed battleaxe, twin shortswords, a two-handed broadsword and a war hammer, respectively. And this isn't even including the magic users or or the Improbable Weapon Users.
In Betrayal at Krondor, any sword-using party member can use any kind of sword imaginable, be it rapier, cutlass, broadsword, or something the programmers clearly made up. However, swords meant for thrusting will be more accurate and powerful when used to thrust rather than swing and vice versa.
In A Beginner's Guide to the End of the Universe, the army of the future people use completely random weaponry (from shotguns to halberds). Justified in that they get all their weaponry from the miscellanopod trees, which give them entirely random stuff. Meanwhile, the members of the evil cult that opposes them are able to use Reality Warper powers to spontaneously manifest any weapons or equipment they want.
Sluggy Freelance: During the "Oceans Unmoving" arc, the Space Pirates use swords, throwing hatchets, flintlock guns, grenades, switchblades, and even laser weapons. Justified since the residents of Timeless Space are literally from different points in history, some coming from the present, others the far future, and others the distant past. Also justified when it's found that most of the 'pirates' are geeks of one sort of another, who took the opportunity of being stranded in timeless space to play pirates, and so picked whatever weapon they felt was cool.
Chaos Fighters are this as a whole, with modern and medieval weapons appearing simultaneously. It gets egregious when bronze coin daggers, scimitars and katana are added. This is not counting the double weapons and mix and match weapons.
Comes into play at points of Tales of MU in Callahan's class, Mixed Melee, in which the main character, variously armed with a dagger, a pitchfork, and a quarterstaff, has to spar against Gloria, a Knight Templar with a sword. The lack of parity is at times remarked upon as well.
The Whateley Universe. Some of everything in this package. Fey now has a magical mithril scimitar. Bladedancer has a magical jian made of jade. Tennyo has an antimatter lightsaber. Lancer is a flying brick and can extend his super-strong field over small things, so he has paper swords... which can cut through concrete. And then Winter Term courses include a 'special topics' class, so this gets really gets crazy. Phase is working with a tactical baton, Chaka is learning the meteor hammer, Aquerna gets a pair of kama, Shroud is working with a dozen knives (simultaneously), ...
In Rollbots, most people who are onvolved in fights have some kind of special weaponry; Botch has a Hard Light grappling hook, Manx has EnergyBalls, Macro has a giant Wrecking Ball, the Kei'zatsu have Hard Light handcuffs which coat the entire body... and Spin has a collapsible sword.