Specifically, I mean films that have some semblance of the same script.
For example, Tarzan is the most frequently recurring character in film, but the films are so different that they can’t be considered remakes. Although Tarzan the Ape Man with Bo Derek is definitely a remake of the film of the same name with Johnny Weismuller, most of the stories of the films are unrelated. Jungle-boy meets city-girl is not enough commonality.
But I would consider two films that are attempting to be screen adaptations of the same source material to be “remakes” for the sake of this thread. In that case, Disney’s Tarzan and Greystoke can be considered versions of the same story since they both are attempting to bring Tarzan of the Apes, the book, to the screen – not just borrowing the characters.
Cartoons count. TV counts.
Films do not have to have the same title when it is obviously the same story and characters.
Change of setting is allowed, but it gets kind of subjective. For instance, I would call The Magnificent Seven a remake of The Seven Samurai. But do we call Forbidden Planet a version of The Tempest? I’m not sure.
But speaking of the bard, I’m sure that the hands-down winner is one of Shakespeare’s plays, probably Hamlet. So let’s leave Bill out.