Beam Me Up, Scotty!: Minor example. Most parodies of the ending scene have every character shout "O Captain, my Captain" when they stand up. In the film, Todd and Knox say the phrase while everyone else stands without saying anything.
An earlier draft of the script included Ginny Danbury, Chet's sister and a friend of Chris's. Along with giving Chris more screentime, Ginny also had the role of Hermia in the play and the actress who played her, Lara Flynn Boyle, still appears in those scenes even though the scenes with her as Ginny were cut. Even though those scenes weren't technically necessary for the rest of the movie, it would've been nice for Chris to have a friend outside of her love triangle with Chet and Knox. There's even a hint at the character, when Chris mentions her to Knox at the party as if wanting to set them up.
Liam Neeson and Dustin Hoffman were considered for the role of Mr. Keating.
Originally, Cameron was supposed to stand on his desk in the final scene like the rest of the Society. However, Dylan Kussman, the actor who portrayed him, felt that this would be out of character and said so to Peter Weir. Weir agreed and so they changed it to Cameron remaining seated.
One early idea was to have Keating be dying of leukemia during the course of the film. This was changed so the film could focus on the boys instead.