What you are basically asking is if there are cellular processes that are thresholded (ultrasensitive). Yes; there are many examples and it would be difficult to list them all.
There are different mechanisms by which such a switch like behaviour can be implemented. Positive feedback loops and co-operativity (in transcription factor binding or enzyme-ligand binding) are common mechanisms by which such switches can be implemented. Have a look at this wikipedia page. For more details you can refer to a book on enzyme kinetics and non-linear dynamics. If you search co-operativity and postitive feedback loops then you will find studies on specific examples.
But as already pointed in the other answer, almost all cellular processes are concentration dependent. There are a very few examples where you can actually observe zero order kinetics.