While the safest choice for a scene like that is to use special effects and make-up, Steve Carell thought that it would be much better if the waxing was real. The reaction the character is having is completely genuine. Carell said that his experience was so horrible that he promised to never do that for a movie ever again.
During the scene where Eowyn stares into the distance, we can see a flag being ripped off a pole and flying away. While this scene may look intentional and metaphorical, the flag flew away by accident but it fit so well with the scene, that it was kept in the final cut.
The scene where Mrs. Doubtfire had to cover her face with icing didn't go as planned. When the icing started dripping down the actor's face because the heat from set lights made it melt, Robin Williams had to improvise. At the moment when the icing dripped into Mrs. Sellner’s tea, he decided to say, “There you go, you’ve got your cream and your sugar now.”
Star Wars: Episode V - The Empire Strikes Back (1980)
In the scene, when Princess Leia tells Han Solo that she loves him, he was supposed to respond by saying "I love you too". However, Harrison Ford felt that this response wasn't suitable for his character, so instead, he improvised and responded by saying "I know".
The director could not stop Robert Downey Jr. from sneaking snacks into the set, so he had no other choice but to make his snacking habit a part of his character. So all the scenes of Tony Stark eating are probably not scripted.
In this film, Anne Hathaway portrayed an awkward and geeky girl who finds out she's heir apparent to the throne of Genovia. While filming a scene where the character was supposed to walk on bleachers with her friend, Anne took a pretty nasty tumble. However, it fitted so well with the clumsy character that this unscripted accident was left in the film.
Leonardo DiCaprio is an excellent actor who doesn't break character even when he hurts himself. He proved that during an intense scene when he hurt his arm with a shard of glass and blood started gushing from his wound. This scene wasn't scripted and the blood was real, it was left in the final cut because of the amazing acting.
The famous line "I am the king of the world" wasn't scripted, it was made up on the spot by the director. After trying several different lines, James Cameron realized that nothing was working and told Leo to just say "I am the king of the world" and really sell it. This scene became probably the most iconic part of the movie.
While filming, Dustin Hoffman accidentally passed gas, however, he and Tom Cruise made it look like it was part of the scene. Actors managed to stay in character and spontaneously created such a good scene that it became a fan favorite.
Al Pacino prepared for his part by not allowing his eyes to focus on anything. He got so good at simulating blindness, that he could barely see anything. The scene on the street, where the actor fell over a garbage can, happened by accident because of his bad vision.
The epic plate throwing scene in this movie was improvised. In the script, Lester Burnham throws the plate at the floor, however, Kevin Spacey decided to violently throw it into the wall right behind Thora Birch's back, landing genuine reactions from the actors in the scene.