20/20 so far. For some reason I though there was only 20.
Edit: 40/40 so far. I got down to last-guess on a couple of them and got lucky with one (random guessing of letters).
Edit 2: 41/42
Edit 3: OK so I randomly hit the keyboard 'til I got to the end. The movies become generally less-well-known and the clues are less obvious. For those interested, the game currently has (inviso follows for those who want a surprise) 81 movies, and they're constantly adding more.