CPL is for controlling polarized light. This can be in the form of reflections off of non-metallic surfaces (like big glass storefront windows or reflections or glare coming off of the surface of water) or for deepening parts of the blue sky - but as Gary points out, its effect is variable across the frame, depending upon the angle of the sun to your camera.
Neutral Density (ND) filters are available in various levels of light attenuation and stop down the light entering the camera, without introducing color shifts. These filters permit the user to shoot in bright conditions at slow shutter speeds - for example, you want that soft silky flowing water effect that takes 1/8 to 1/4 sec but you cannot shoot it in bright light because even at f/22 and ISO50 the shot is still blown by 3 stops? Use a ND filter that gives you 3 stops of light attenuation and there you have it!
Graduated Neutral Density filters (GND) are the same as ND filters but have the "ND" part applied to a portion of the filter. This permits the user to selectively attenuate the light in part of the scene, while letting the full amount of light through form the rest of the scene. In terms of HDR and DR compression, this is the filter that would achieve such an effect. So, if you have a super bright blue sky and your "ground" area has lower brightness details in the midtones and shadows, you could use a GND to attenuate the light in the sky (the upper half or third of the scene) and let the full amount of light through for the rest of the scene. This effectively compresses the dynamic range of the scene by locally changing exposure. It is sort of like a real-time exposure blend where you would normally take one shot for the sky and another shot for the ground and then blend the two in post. Of course, you have to choose the correct amount of light attenuation to achieve the compression you want.
I do not use any of these filters when shooting HDR. However, some applications (like Picturenaut) permit the user to enter a value for the effect of a filter so that the EXIF data are corrected to the actual exposure based on the amount of light that the particular filter is attenuating during capture.
Kirk