Pre-Devil May Cry series
Sharing its name with its wielder, the Sparda Sword was the weapon Sparda used to defeat Mundus and save the Human world, the same feat Dante achieved two thousand years later. To prevent the many Demons with aspirations of world domination invading again Sparda sealed off the entrances between the two worlds. With his own demonic power sealed with them the Sparda sword reverted to the Force Edge, awaiting the day when it would be used once again.
The awakening of Temen-ni-Gru
In Devil May Cry 3/ Special Edition Sparda's son Vergil sought his father's legendary power. Aided by Arkham and with the Yamato sword by his side, they set about the motion of events that would lead to Temen-ni-Gru arising so that they could unlock the Demon world, knowing that it would attract Dante with his half of the Demon world amulet. Once he served his purpose Vergil apparently disposed of Arkham, only for Arkham to assualt the heavily weakened trio of Dante, Vergil and his daughter Lady. Arkham was the first to make his way into the Demon world and aqquire the Force Edge for himself. Even in its weakened form, the Force Edge possesed latent demonic power, tranforming Arkham into a monstorous demon. This proved to be only a minor set-back as the sons of Sparda defeated him, sending him crashing back to Earth where his daughter awaited to kill him.
After a brief struggle, Vergil emerged next to claim the Force Edge, and battled Dante to take his half of the amulet and transform the sword into its true form for the first time in almost two thousand years. Alas, Vergil fell to Dante wielding the Rebellion. His plans having failed, he then chose the live in the Demon world, his half of the amulet in hand. Dante left and became the new owner of the Force Edge.
The return of Mundus
Years later, during the events of the first Devil May Cry, Mundus attempted to take the Human world once again. With his demon generals (which included a corrupt Vergil) he arose in Mallet Island and sent Trish to find the other son of Sparda in order to turn Dante to his side or destroy him trying. The older and wiser Dante, Force Edge in hand, proved too much for all who stood in his way. For some time, Dante took to the using multiple devil arms, including Alastor and Ifrit, but after defeating Nelo Angelo and the revelation of his identity, Dante took both halves of the Demon world amulet, combined them and transformed the Force Edge into the Sparda sword. This increased Dante's power to the point that his Devil Trigger resembed Sparda himself in looks and demonic strength.
After besting Mundus, Dante left his sword and amulet in the care of the fallen Trish in respect for her sacrifice and newfound human qualities. This proved to be a wise descision, as Trish survived, made her way back to the Human world using the amulet and assisted Dante in banishing Mundus from the Human world once and for all.
Bringing Sparda into the spotlight
Trish continued to use the Sparda sword while Dante returned to using the Rebellion until the events of Devil May Cry 4, in which Lady informed the duo of the Order of Sparda, who were taking devil arms for their experiments and unlocking gates to the Demon world. Trish infriltrated their organisation from the inside, gaining their trust with the Sparda sword while Dante set about closing the portals. The leader of the Order of the Sword, Sanctus, took the Sparda sword for himself, increasing his powers far beyond that of his Angelo Sanctus form. In the end he was still no match for Nero and the Yamato who killed him and then finished off the Saviour.
Nero returned the Sparda to Dante, but was allowed to keep the Yamato after impressing Dante (who may or may not know about the link between Vergil, Nero's arm and the Yamato).
Currently, as of the events in Devil May Cry 2, Trish and Dante have resumed using the Sparda and Rebellion respectively.