It's worth noting that ND filters can also be stacked, assuming their screw fittings are compatible. Their effects then multiply - so two 4x filters will have the same effect as a single 16x ND filter, and adding a 4x to 8x will give you 32x. In other words, purchasing both 4x and 8x ND filters will place three different levels of ND at your disposal, giving you plenty of shooting flexibility in different lighting conditions.
Of the two possible effects of ND, the aperture flexibility is the most useful. Video already has the tendency to look flat, and having a wide depth of field merely accentuates that. Ensuring focus is concentrated on your subject matter, with background and foreground fuzzy, keeps your viewers' attention on what you want them to look at. It will also make focus pulling much more effective. This is where your camera focus switches from something in the foreground to something in the background - a great way of leading your viewers' attention for dramatic effect, and rather reduced if both foreground and background are already reasonably well focused!
In the two images above, you can see the effects of just a small amount of ND. On the left, everything onscreen is in focus. The intended subject (the plaster otter) is as clear as the two bricks, and the concrete background. In the right-hand image, however, a 4x ND filter has been applied. Now only the otter is fully in focus, with the more distant brick quite fuzzy and the background much softer.
Camcorders can also be susceptible to picking up haze, again in very bright conditions. Here, a Skylight filter reduces the effect and cuts the amount of blue, improving colour balance and warmth. We would recommend 1A or 1B strengths. An Ultra-Violet (UV) filter can also help reduce haze, but without the colour balance benefits. If you shoot a lot of landscapes, a Polarizing filter will make skies look a deeper blue, and reduce surface reflections and glare. None of these effects are easy to replicate with editing software, and may even be impossible. But the appropriate filters are only around a tenner apiece.
Another filter you may want to consider is Soft Focus. Consumer camcorders often use a lot of video sharpening to give the appearance of crispness. But this can cause unwanted artefacts round the edges of objects. Some premium models give you the option of reducing this. For example, Sony's HDR-HC9E offers sharpness control, and a number of Canon's camcorders bundle reduced levels of sharpening with their image effects presets, such as the HG10.
For camcorders without this level of control, you can subdue unwanted sharpening by adding a soft focus filter. This can reduce the ‘hyperrealism' of video and make it look a little more like film. Of course, it may be possible to add this later in your editing software, but that will have a processing overhead. If you're sure this is the look you want, adding a mild soft focus filter to your camcorder will only set you back around a tenner, again from the likes of Keene Electronics or Jessops.