Arnold Schwarzenegger's famous line in The Terminator 'I'll be back' was originally scripted as 'I'll come back'.
The scene in Ghostbusters where Venkman sees Slimer for the first time and "drops his jaw", his cigarette sticks to his lower lip and dangles. This was a complete accident during filming, but turned out to be awesome anyway, so they kept it. That scene for me is one of the most memorable things I've ever seen in a movie, and it was never intended to be there!