Any filter that changes properties of the light that isn't captured by the digital sensor (or film), is impossible to reproduce in post-processing.

So:

• A polarising filter removes light beams with a specific angle. As the sensor doesn't record the angle of the light beams, it can't be recreated in post-processing.

• An ultra violet filter reduces light above a certain frequency. As the sensor doesn't record this frequency range separately, it can't be recreated in post-processing. However, as digital sensors are less sensetive to UV light this is not a big problem for digital cameras.

• A neutral density filter doesn't have any filtering effect, in the sense that it affects all light the same. The desired effect is to change the exposure time or aperture, and the effect of that can not be reproduced in post-processing.

• Any filter that changes the path of the light, like starlight filters, is impossible to recreate exactly in post-processing.

However, some of the effects of those filters can be emulated, like getting the dark blue sky produced by a polarising filter, or getting something that looks very close to a starlight filter.

Some filter effects is actually easier to use in post-processing, like positioning a gradient filter exactly where you want it.