I was just wondering how (un)common it is to start filming a movie before having the screenplay finished and sort of write it as you go along. Is there a list of movies that were produced in that way?
I can't talk about how common or uncommon it is for a movie to being filming without the screenplay being completed, but I can give an example of it happening;
The Marvel Studios film Iron Man (2008) quite famously "had no script".
In an interview with Jeff Bridges (who played Obadiah Stane), he claimed;
They had no script, man... They had an outline. We would show up for big scenes every day and we wouldn’t know what we were going to say. We would have to go into our trailer and work on this scene and call up writers on the phone, ‘You got any ideas?’ Meanwhile the crew is tapping their foot on the stage waiting for us to come on.
Other than that, I'm not really aware of any movies that have found themselves in a similar position - but the way that Jeff Bridges talk about it implies to me that a movie beginning to film without a script is a rare occurrence.