Quite a few.
It's nothing like the analogy you use at all. Film needs CHEMICAL processing to realise the latent image, of course. The correct analogy would be liking that chemical process to the digital conversion of the data into visible pixels on the screen. Beyond that is where YOUR analogy begins: Processing as you mean it here is the equivalent to the printing of a slide or negative. While there are a few things you can do during the chemical process to alter the image (c41 to E6 or vice versa being the most common) most other manipulation of the analogue image was done post-process... just like it still is.
So yeah... quite a few Pete. If all I want is an accurate record of something, I will not process at all beyond white balance. If I did, it would no longer be accurate.
You speak as if there's no use for a straight from camera image