Neo Geo who became popular for 2d fighting games, give us Samurai Showdown; the first of many sequels to come then Samurai Showdown 2, 3, etc. I think it was the first fighting game I played that involved swords.
This video is a sample of games emulated on the PSP. In this case I have "Samurai Showdown"; a great classic game from the early 90s. There are hundreds of games for the NEO GEO alone.