Fate/stay night is the VN that started it all, it now has two anime and a movie (which I have heard is kind of confusing), Fate/Zero the LN turned anime, and a few other LNs including Fate/Apocrypha.
I totally recommend Fate, and I suggest you start by Fate/Zero (due to chronology) and then move to this year's Fate/Stay Night - Unlimited Blade Works. It is still ongoing, but up to now it is much superior to the original one.