Optical Filter Benefits

With sophisticated image editing tools like PhotoShop readily available, why bother with optical filters? Given enough time, talent and patience, you probably could emulate most filter effects in post-processing. Post-processing is no substitute for the filter types listed below — at least when they're properly applied.

Polarizers	Among other things, polarizers can easily save you from fatal white-outs due to bright reflections — not just off water, glass and car paint, but also off foliage. (Foliage reflections are a serious but commonly overlooked problem in landscape work.) The hard fact is, there's not good post-processing cure for white-outs, especially those complicated by CCD blooming. Polarizers can help you control excess contrast in other ways as well. They also improve color saturation in ways hard to reproduce at post-processing.
Neutral density (ND) filters	ND filters allow you to achieve slower shutter speeds or wider apertures than would otherwise be possible in a given scene. (Note that polarizers make decent 1-2 stop ND filters in the absence of polarized light.)
Graduated ND (GND) filters	GNDs allow you to reduce excess contrast in scenes that would otherwise be impossible to capture in a single shot. Yes, there are effective post-processing techniques for excess contrast control, but they're not without their challenges, and most require multiple perfectly registered exposures — which means a tripod and remote triggering.
IR pass and UV pass filters	Even if you could simulate the surreal luminance relationships found in the near IR (NIR) in post-processing — you'd never be able to fake the phenomenal atmospheric clarity found at NIR wavelengths. Nor would many be able to fake the odd world waiting to be discovered at UV-A wavelengths.
UV cut filters	In theory, UV filters add clarity by cutting UV scatter in high UV environments — e.g., at extremely high altitude (well over 10,000') or in long shots over water, but most digital cameras are too UV-insensitive to benefit here. Post-processing can suppress or sharpen a hazy blue channel to good effect, particularly in B&W work, but an effective UV filter (most likely a haze filter) might allow you to improve clarity while preserving blue channel data in your color images.