The Masamune sword is featured in many games that I’ve played over the years, from Soul Calibur to Chrono Trigger to Final Fantasy.
It’s a sword that is usually surrounded with some sort of magical property or regarded as something very powerful, yet mysterious.
Is there a specific origin of this sword? Is it based off of a real sword that exists today? Why do multiple video games use this same sword?
The name Masamune doesn’t reference an actual sword, but a legendary sword smith called Gorō Nyūdō Masamune. (Altough, his name is also attached to his swords, like Honjo Masamune, Fudo Masamune, Hōchō Masamune and Kotegiri Masamune.) And for this to make sense, you need to understand that Masamune isn’t regarded only a great swordsmith, but the great swordsmith. You can read more from the linked Wikipedia-article.
The same hold true for his pupil, Senji Muramasa, whose name you’ve no doubt also heard in similar contexts. (Pupil as supposed by legends, actually, as some sources state that they didn’t even live at the same time periods.)
Masamune’s and Muramasa’s names are widely used in Japanese popular culture to refer to either legendary swordsmiths or swords. So much so, that this has became a sort of cultural meme.
Something I see often is western game developers, who most likely know the names only through games, using these to refer to only swords, as opposed to people.
For more on the cultural side of the two names, mostly their use on swords, see their TV Tropes article (beware of getting lost on that site).