Late last year, inspired by some of the long-exposure photos by Tasmanian photographer Alex Wise, I bought a B+W ND 3.0 filter.
It is a neutral density filter with an ND 3.0 rating, which means it reduces the exposure by 10 stops, letting just 0.1% of light through. In other words, it's an expensive piece of dark glass!
I bought a 77mm sized filter, to fit my Canon EF 24-70mm f/2.8L lens and Canon EF-S 10-22mm lens.
An ND filter reduces the amount of light allowed through the lens, thus allowing the use of much longer shutter speeds during the day.

Here is one of the first photos I took using the 10-stop ND filter. This is a beach scene at Point Peron, taken about half an hour before sunset, in January. The ND filter allowed a 30 second exposure with a fairly wide aperture of f/5.6. A long exposure on such a scene serves to completely blur the waves, resulting in a flat ocean, and milky/smoky water where the waves were breaking on the beach. Due to the movement of the clouds during the exposure, they are also blurred, providing a streaked look in the sky.

long exposure at Point Peron

Point Peron, Rockingham, Western Australia
Canon EOS 50D, 10-22mm @13mm (10-stop ND filter), 30 sec, f/5.6, ISO100

I am very happy with the results, and will need to make some additional opportunities to use the 10-stop ND filter, particularly for beach scenes and waterfalls.