mct16:
he only one that springs to mind is Bogart's "The Maltese Falcon" which was actually the third film version of Hammett's novel.
Funnily enough, this was what went through my head too, when I first saw your thread title - and I've never managed to catch
Satan Met A Lady, which was the second one made, with Bette Davis in it.
However, this is partly the crux of the matter, and touched on in the article that blueskirt linked to above: what is a "re-make", and what is just a different version of another source?
Strictly speaking, the three
Falcons are actually just variations on the same book; the middle one is apparently a light comedy thriller, while the third is a hard-boiled (albeit wittly scripted) detective film.
Even the Moviefone list is inconsistent, as it says that Pacino's
Scarface is a remake of the earlier Edward G. Robinson movie, when about all they share is a title: Robinson plays a thinly disguised Al Capone, whereas Pacino plays (
really badly!) a Puerto Rican drug dealer. Same name, entirely different premise.
It's the same for things like the
Ocean's Eleven movies - they share a name, and little more (and both are pretty dumb) - and the two
Italian Job films (I like the newer one more than the original).
It is interesting to look at the
Thomas Crown Affair; I agree with the list that the re-make with Brosnan and Russo is a more polished film. However, why not compare that and the original film to
Entrapment, an "unrelated" film, which actually has the same premise (insurance agent sent to investigate suave criminal who can't be caught falls for the man she is investigating - or does she?). It is far more akin to a re-make of
Thomas Crown than the two films called
Scarface are of each other.
For
true re-makes, there is one sequence I can think of, of films where the original has a re-make, and the re-make has a re-make, and they are all actually good and interesting films: the Douglas Fairbanks 1920
The Mark of Zorro (admittedly based on a novella) was remade for sound in 1940 (ditching Don Diego's mute servant in the process), with Tyrone Power; that was then remade for TV in 1974, starring Frank Langella, and retaining most of the 1940 version's script verbatim, much of its score too, and even some of the same locations. They are about as close as I can think (outside of exercises like the
Psycho shot-for-shot treatment) of the same film being remade time and again.