One I would recommend is the old BBC Drama series from the 70s called 'I Claudius'. It's about the man of the same name who would eventually become the emperor of Rome - and who actually did stutter in real life. I can't speak for how accurate Derek Jacobi's stutter is, but I know he did spend time studying from someone he knew who actually had one. I Claudius is an interesting depiction in that it while it explores how *other* people see Claudius as an idiot, an embarrassment or a joke - he himself is clearly shown to be one of the most intelligent and canny members of the imperial court. I always thought that [this scene](https://www.youtube.com/watch?v=FQe28wNe6SU) was a great demonstration of the above (some spoilers).