Depending on how you look at it, either a very large knife or a short sword. Made from solid gold it is an expensive weapon. And for those who seek it, expensive can also mean costly...
Originally forged by Neoldian at the request of the trickster-goddess Errata and flung into a gathering of eighty-odd War Gods and divine representatives of allied trades, with a label attached to the hilt saying "For the Strongest". (Δυναμιστι) The fight failed to break out, as Neoldian had also engraved Lagunculae Leydianae Non Accedunt - "Batteries Not Included". Only two gods fought for it - Patina, goddess of Wisdom who claimed it was a subtle metaphor for the hopelessness of existence and Cephut, god of Cutlery who claimed it was a big knife.
Locating and securing this weapon is the raison d'etre of the computer game Discworld Noir. The Falchion is the artifact that can give Nylonathatep infinite power or destroy it. The weapon is linked to a jewel called the Radiant Trapezohedron: it has an indentation in its pommel, where the can be fitted, giving it its power to destroy Nylonathatep, and when they are separated, the jewel always shows an image of the sword's current location.
Mundy, in an arrangement made with the Followers of Anu-anu, smuggled the sword to Ankh-Morpork in the Milka, but made plans with Jasper Horst later to give it to him. Mundy got killed but the weapon wasn't stolen from him, because he had sent it to the Guild of Archaeologists to keep it safe. Inspector Lewton finds the sword in the vault 51 of the guild but Horst steals it from him, but Lewton finds Horst again and throws him to the river Ankh, reclaiming the sword. Finally, with the trapezohedron and the sword, Lewton throws them from a flying device to the summoned Nylonathatep, destroying him.
Regard the Greek trickster goddess Eris (Roman Discordia) throwing the golden apple in among the goddesses with a label attached saying "For The Prettiest" (Kallisti), thus causing arguably the biggest and most unseemly cat-fight ever.
Another candidate is the will of Alexander III. On his deathbed in Babylon, he was asked who should succeed him as king. His answer was "The Strongest". Resulting in the wars of Diadochs. Which arguably went on for over 50 years. The Trojan war was over in 20 years after the apple-throwing (10 of the Achaians could not figure out where Troy was).
"The Maltese Falcon", whilst not being a sword, is an objective for private eye Humphrey Bogart in a Roundworld film noir.
("For the Strongest" - a translator suggests dynamisti. Thank you for assistance in the Ephebian letters!)