The anime is based on a visual novel that has three routes, three different ways the story unfolds. The original Fate/Stay Night anime adapted the first route, the Fate route, but did a poor job of it and you can just skip it altogether. UBW is the second route, covered by the recent series (though there is also a movie version, but that's not worth watching). The third route, Heaven's Feel, is getting a movie trilogy adaptation. This one, Zero and the UBW series are done by studio Ufotable and cover the original story and are arguably all the Fate anime you need for the story proper. Beyond that, there are numerous alternative versions and extras.
Fate/Aprocypha is one such variation. It takes the general established notions and plays with them, placing them in a new setting and doubling the number of servants. It's not all that good.
Fate/kaleid liner Prisma☆Illya takes the characters and places them in a mahou shoujo setting focusing on Illya.
Similarly, Fate/Extra Last Encore and Fate/Grand Order (both of which are based on games) play around with the setting.
Additionally, there is also Fate/Prototype, which is a preview of the original concept idea. The Fate/Stay Night VN was originally intended to have a female protagonist and would have been without a gender-bent Arthur. This short showcases how it would have looked like.