Actors that directors let improvise their dialogue?

It is my impression that many of our modern major stars are allowed great latitude to improvise on set. I'm talking Dustin Hoffman, Robert DeNiro, and the like. Whether their improvisations remain in the movie is another matter. They probably don't have any guarantee. A very famous example is the "You talking to me?" scene from Taxi Driver. It was not in the Paul Schrader script and was even left out when the script was published in book form.

There's the famous scene in "The Empire Strikes Back" where Harrison Ford replies simply with "I know" when Princess Leia confesses her love. The original script had Han Solo reply with something different.

Director Irvin Kershner loved it and it stayed in.

I think I read that Brando wouldn't use the script for APOCALYPSE NOW so Coppola let him ramble on for hours and then used whatever seemed vaguely coherent for the Col. Kurtz scenes.

I have a feeling that Cary Grant was free to improvise under both Alfred Hitchcock and Stanley Donen as long as they got the shots the directors wanted.

Reading through Ernest Lehman's North By Northwest script, quite a few instances can be detected in which Grant deviated from the dialogue as written.

Grant kept a suite at the Plaza Hotel, in which he stayed while the production was on location in NY. There's a story repeated in several books on Hitchcock that when a scene in which Grant walks across the Plaza lobby was ready to be shot, he was called in his suite, came off the elevator, went to his mark, the cameras rolled, and after Hitchcock called, "Cut," Grant got back onto the elevator to return to his suite and await summoning for his next scene. A visitor to the set expressed astonishment that not a word had been exchanged between Hitchcock and Grant, to which the director is said to have replied, "Oh, he's been walking across this lobby for years. He doesn't need me to tell him how to do it."

Another story has it that when Grant went to inspect the Twentieth Century Limited stateroom set, he found it inadequate, reporting to the director, "Hitch, you can't shoot on that set as it stands," and Hitchcock ordered the set rebuilt purely on Grant's say-so and without even going to look at it.   
  

I'm surprised Robin Williams' name hasn't popped up. Or Jim Carrey's.

Robert Altman