I can’t no one has yet mentioned two of the most famous examples:
“Taxi Driver” – Robert De Niro’s “You talkin’ ta Me??” speech in front of the mirror was completely ad libbed. It was supposed to be a two second shot of Travis Bickle aiming a gun at his reflection in the mirror, but while filming De Niro stayed in character and kept talking. Now it’s one of the most famous scenes in movie history.
“The Shining” – Jack Nicholson’s famous one-liner “Heeeeeerrrreee’s Johnny!” as he’s hacking down the bathroom door was also ad-libbed. In fact, director Stanley Kubrick (who lived in England and never saw “the Tonight Show”) didn’t even get the reference and had to be talked into keeping that scene.
This reminds me of “On Her Majesties’ Secret Service” - the one and only George Lazenby/ James Bond flick: Supposedly, he was such an egomaniac on the set that his co-star Diana Rigg chewed cloves of garlic before filming every love-making scene so that her breath stank whenever he had to kiss her.