Ali ibn Abi Talib, Muhammad's cousin, commander during the early years of Islam, and eventual Caliph, fought with Dhu al-Fiqar (sometimes written Zulfiqar), a sword that was bifurcated at the tip. It was shown in the movie The Message stylized as such.
Attila the Hun wielded a sword he called the "Sword of Mars". Im on my phone and in a foreign country, but I believe the sword was "discovered" in a field and used by Attila for his campaigns in Gaul. The use of quotation marks is to denote the fact that this information was most likely propaganda spread to both terrify his opponents and legitimise his own position within Hunnic society
I don't know how far you want to go back but the US General from World War 2 named George Patton was famous for carrying an Ivory handled Colt revolver.
Also during World War 2, "Mad Jack" Churchill was famous for chargeing into battle with a ceromonial sword as seen famously here, he is on the far right.
Guan Yu, a general of Shu during the Three Kingdoms period, is purported to have carried a sort of polearm called the Green Dragon blade. However, the main source of this is the Romance of the Three Kingdoms, which is a pretty fictionalized history of the Three Kingdoms period. So we don't really know if this weapon existed or not. There is a weapon called "guandao," that is supposedly derived from this polearm, but there isn't really any corroborating evidence to this hypothesis outside of RoTK.
Roland was one of Charlamagne's Paladins (think French version of knights of the round table). He carried a sword named Durandal which according to legend was unbreakable.
You might be interested in the Sword of Goujian. Although I don't think historians know for certain who the sword actually belonged to. There are 9 kings that the sword could have belonged to.
Charlemagne, famously, had Joyeuse. I believe it still is around.
This historical list is exactly what you're looking for.
Japanese swords exist and there is a nauseating long list somewhere on wikipedia of famous Japanese katana. but I didn't dig for that. You should be able to find that from that list.
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EDIT:
I don't have ton of time nor my resources in front of me but here's the paraphrase of Ewart Oakeshott from his work concerning swords and archeology:
Germanic, Gaulic, and Celtic cultures used swords as status symbols, especially prior to steel, which were associated with wealth and power but were more of a side arm. Spears saw more action and were more likely to be replaced over time due to use while the status symbol might last longer though not if used regularly in combat. Those that did last may attain a sort of cult status after their owner died and become more mythic in the telling of the person's life. The Romans did not have a romantic tradition concerning swords in the same way but as the Roman and 'barbarian' cultures and traditions merged (and the medieval Christian relic craze may have helped) and personal weapons became important. The classic example is Charlemagne and his sword Joyeuse and Roland and his sword Durendal. While the latter is unlikely to actually have existed; there is enough secondary sources which indicate Joyeuse was real though that leads to point two.
Weapons are tools and see rather harsh use. They can get lost in the field, break, need repair, etc. The historically associated 'X's sword/spear/etc' are either ceremonial weapons (such as the actual Joyeuse) or are burial weapons. Ceremonial weapons are the most common 'museum piece' because they are works of art and meant to show power, wealth, and status. The exception is weapons for bodyguards which tend to be both very functional and pretty to look at (the use of larger weapons for the job meant more space for decoration without needing to use particularly expansive methods and instead stick to lacquer and etching). Burial weapons tend to be a good quality weapon of the type the person was associated with and would use (either actually buried with them, worked into burial art, or both). For example, Edward the Black Prince's tomb has a sword in the decoration which matched the one he was buried with (though it was later lost and found). Considering the preferences of a prince, it may be he used swords made identical or similar to it throughout his life but it is unlikely it was the same sword (barring the "I've replaced the blade twice, the pommel once, and the cross guard three times, but it's my sword!" style of arguement) and this could be said for many other powerful people.
El Cid/Rodrigo Diaz de Vivar (c.1043-1099), National Hero of Spain, had a sword called Tizona. http://en.wikipedia.org/wiki/El_Cid#Swords
Hang Tuah, a legendary warrior and admiral of the Malacca Sultanate, wielded a kris named Taming Sari (Beautiful Shield) which was said to make the wielder invulnerable. The kris purportedly still exists as part of the royal regalia of the Malaysian state of Perak.
I haven't been able to find any sources online, but it's a well-known legend amongst Malaysians and is in part told in Sejarah Melayu, the Malay Annals, and Hikayat Hang Tuah, or the Stories of Hang Tuah - a romanticized collection of tales much like the Romance of the Three Kingdoms.
Two images of it I found via a cursory Google search: http://imgur.com/a/Yo1sy