I believe the same is true of A Man for All Seasons: the 1966 version with Paul Scofield and the 1988 made-for-TV version with Charlton Heston.
I must confess that until I saw the TV version, I had no idea the first movie was adapted from a play.
Never Say Never Again is an acknowledged remake of Thunderball - same plot, same characters, but a few minor differences here and there.
Interestingly, it legally had to be pretty much the same film because Kevin McClory only had the rights to remake Thunderball and not come up with a new James Bond adventure of his own, as I understand it.
The Hal Hartley movie Flirt, starring Parker Posey, is made of three sections (set in New York, Berlin and Tokyo), each section using the exact same dialogue, but with very different meaning.
(It also features a fantastic line my best friend and I have been quoting at each other ever since we saw it: “Your problems are trivial”.)
In Heston’s autobiography it is apparent he wanted the movie role so badly he could taste it, but when it went to Scofield he graciously accepted it, as he respected the guy. He also noted how Scofield actually bore a close resemblance to the Holbein portrait of More. Heston acted the play more than once on stage as well, and once his wife Lydia played opposite him as Lady Alice.
See Post #4
Do screen adaptations of plays count? Like all the Shakespeare stuff over the years? Or will we not count those because of the “adaptation” part?
Just wondering…
“Titanic” seemed somewhat deja vu to me, one of the previous movies about the Titanic seemed to have been a big influence on the Leo/Kate version. Minus the shipboard romance, of course. Or maybe I’m all wet here. 
Nick Knight was originally filmed as a vehicle for Rick Springfield, but it went nowhere. Then I happened to catch a show called Forever Knight with the same plot and dialogue but with different actors (except for one who made the second cut).