National Weapon

""Did you see those warriors from Hammerfell? They've got curved swords. Curved. Swords.""

- Guards, The Elder Scrolls V: Skyrim

Just as cultures might have an iconic Battle Cry attached to them, often they will have a weapon that has a similar status. Sometimes it will have a religious or magical significance; it might for instance be a copy of a blade that was Forged by the Gods. Perhaps it typically has a Badass Creed engraved on it. Or maybe it is simply hard to imagine them fighting without it, and even if it becomes obsolete it is impossible to imagine this group parading without it because it has a symbolic status that goes beyond its functionality. As Tropes Are Flexible, this does not have to be a whole culture's weapon; it can be the weapon of any group: say, an order of Warrior Monks, or a Caste or a Secret Circle of Secrets, or a gender. The point is that the weapon is so much connected with a group that it serves as a logo as well as a weapon.

Likely to be wielded by a Proud Warrior Race. If the weapon in question is a physical part of an alien race's anatomy then see Natural Weapon.

Film

 * In Star Wars, the Jedi Order uses lightsabers. The various incarnations of the Sith Order also use lightsabers, universally colored red.

Literature

 * Dune crysknives made from the tooth of a sandworm are sacred to Fremen.
 * Dwarves use Axes in Lord of the Rings
 * Also based on Tolkien is the association of Elves with bows, which is less supported by the original mythos (Tolkien's Elves are good with bows, but for the most part they prefer swords).
 * Based (as always) on Tolkien, the Dwarfs of the Discworld consider their battleaxes cultural artifacts, and will not part with them even when circumstances require them to bequeath all other weapons (at a diplomatic function, for instance). In Thud we are introduced to a more liberal sect of Dwarfs who do not carry these, believing that the axe is "a state of mind". It helps that they've invented kung fu. Trolls also have clubs, to a lesser degree (a ceremonial club was a minor plot point in Thud).
 * The Aiel in Wheel of Time use knives and bows, but prefer the short-spears, and will not touch a sword under any circumstances. This is revealed as a plot point in the backstory, as there is a specific reason for this reluctance.
 * On Gor a few Fantasy Counterpart Cultures have trademark weapons.
 * The Wagon Peoples [sic] of Southern Gor have the quiva, a set of throwing knives. They also use the bola and lance from kaiilaback.
 * Torvaldslanders (Vikings) have the battleaxe
 * Tribes in Darkest Gor use the "stabbing spear."
 * The Alar (kinda-sorta Roma) have the francisca, an ax different than the Torvaldslanders.
 * Tribesmen in the Tahari desert (Arabs) have the scimitar.
 * Red Savages (Native Americans) hve the tomahawk, as well as the War lance they use from aiilaback. (A different species of kaiila than the Wagon Peoples use.)
 * The caste of Peasants, the lowest caste on Gor, have the quarterstaff and longbow, which are looked down upon by the caste of Warriors but can be quite effective.
 * Rare in Honor Harrington as modern weapons are often not very romantic. One or two cultures have archaic weapons as part of a dignitaries court dress.
 * In Vorkosigan Saga Vor males have two swords when they are really playing dress up even though those are only good for dueling nowadays and there hasn't been a duel heard of in ages. Vor females have a Vorfemme knife. One Vor woman jokes to another that Vor men get swords but Vor women only knives but a knife is more practical in a technological world and could be very useful in the situation it is theoretically for.

Live Action TV

 * The Minbari Denn'bok in Babylon 5.
 * In Star Trek, the Bat'leth functions as this for the Klingons. Interestingly Vulcans, though no longer a Proud Warrior Race still use Lirpas in ceremonies.
 * The Mek'leth dagger too for Klingons though it is not quite as iconic.

Tabletop Games

 * Aslan in Traveller actually use claws in duels, both real and sporting. A human who is Going Native with them, or just wants to be polite uses a pair of artificial claws called Ayloi.
 * In Dungeons and Dragons, many deities have a preferred weapon that their followers tend to use. For example, the holy symbol for Kurbag is a double - bladed axe.
 * In 3rd Edition, the Spiritual Weapon spell summons a weapon made of pure force that is described as taking the form of the user's deity's favored weapon (or a form specific to alignment for characters without a deity).

Video Games

 * In Fallout: New Vegas, The tribes in the Honest Hearts DLC each have a signature weapon. The Whitelegs use .45 Submachine Guns, the Dead Horses use War Clubs, the Sorrows use Yao Guai Gauntlets, and the New Canaanites use .45 pistols.
 * In Command and Conquer: Red Alert, there are two each for the Allies and Soviets. Tanya and the Chronosphere for the former, Apocalypse Tanks and the Iron Curtain for the latter.

Real Life

 * Boomerangs for Australian Aborigenes.
 * Claymores for Bonnie Scotland
 * Katanas for Japan at least for Samurai
 * Shuriken for Ninjas
 * Kukris for Nepal, famously with the Gurkha soldiers.
 * Longbows were once this for the English and the Welsh (they even continued to use them while other nations adopted early firearms), to the point that the longbow design which all of Europe used is known as the English or Welsh Longbow (despite it not being the native bow of either nation).
 * Composite bows for Mongols
 * The Pennsylvania Long Rifle was this for Appalachian Frontiersmen.
 * The Pilum and Gladius for Rome
 * The Hoplite shield for Greece was not primarily offensive so was possibly "armor" rather then a weapon, however hoplites regarded their spears as expendable but treasured their shields.
 * Short spear and leaf-shaped shield for Zulus
 * The Sikh Kirpan dagger is one of the best examples of this for it a symbol of Sikhism representing their obligation to defend one another. Also the curious Chakram ring-knives, often worn in their turbans.
 * The Kris of Indonesia.
 * The Irish shillelagh.
 * The Tomahawk and the Gunstock War Club among Native American/First Nations peoples of the Northeast and the Great Plains.
 * The flag of Mozambique sports an AK-47 with bayonet attached.
 * The pike and to a lesser extent the halberd for the Swiss.
 * After the Mongols overthrew the Rurik Princes, the Russian peasants who were surviving in the forest would hang their axes next to their icons giving them a sacred imagery. Axes are of course tools useful either for chopping wood or chopping people.
 * The Spanish Navaja knife was once almost universal. When medieval monarchs decreed that swords must be possessed by commoners for militia use, peasants couldn't afford them so they presented their navajas to the inspectors and got a pass, presumably because they looked nasty enough to do for its purpose. It got something of a reputation as an underworld weapon, similar to the switchblade in America. However some Hildagos liked them and there are stylized versions to be found.
 * The Roma have a fighting style based on scissors.
 * This is a list of the national knives of Europe, some of whom are primarily weapons and all of which can be used as weapons(if sometimes not all that effectively) http://www.knifeplanet.net/iconic-knives-in-europe/