50/50
If you saw 50/50 with Joseph Gordon-Levitt and Seth Rogen, you probably remember the scene where the main character decides to shave his head after getting diagnosed with cancer. Rogen later explained that this part was actually not in the screenplay. Apparently, they just thought of it while they were in the middle of the shoot. They must have been nervous since they only had one shot to do it right. Luckily, everything went well and it was used in the movie.
Borat
When you have the eccentric Sacha Baron Cohen playing the main character, it’s not hard to imagine that there was a lot of improvisation involved. That was how it was for Borat. One example would involve Cohen and a team of feminists. He tells them that every woman has a “brain the size of squirrel”. While it was off the cuff, it was the perfect addition to the scene.