I started to use neutral density (ND) filters a few years ago - beginning with a graduated one to combat too-light skies and too-dark foregrounds, and eventually moved on to quite dark ND filters that have enabled me to produce long exposure shots. My collection has grown, and I now own the ND graduated one, and three pieces of what's sometimes called "black glass", varying in their blackness. The first one I got is probably my favourite - the B+W 10-stop ND filter. This allows me to shoot for 30 seconds or more in broad daylight and capture moving clouds and smooth water. I found it a bit restrictive (too dark sometimes), though, so added a 6-stop and eventually a 3-stop to my collection, allowing me to have more control over the creative process (more aperture/exposure length combinations were now possible). Occasionally I'll combine a couple of the filters to create an even longer exposure, or something inbetween what each one would allow on their own. I also use a circular polarising filter, which can also have the effect of reducing the incoming light, allowing slightly longer exposures again.
Below are a few examples, comparing normal shots with long exposure shots. The first pair was taken just after sunset in the Cairngorm Mountains in Scotland at the end of April 2011. The first shot was a 2-second exposure (not exactly short, but not that long either), just using the graduated ND filter. The second shot is a 52-second exposure, using the graduated ND filter and the 10-stop filter. They're both taken at 10mm on a cropped-frame camera, and I had to crop the shots as there was a bit of the edge of the filters showing (you cannot shoot that wide when you have filters stacked at the front of your wide-angle lens).
This was the first time I really got to play around with the 10-stopper and I loved it! My opinion is that the second image looks far more atmospheric and pleasing to the eye. As the water was still, there's not a great deal of difference there, so most of the effect is in the clouds. We camped just next to this little lake, and I almost got hypothermia in the process of taking a long series of similar shots (always wrap up warm when taking time-consuming long exposure shots outdoors - especially in Scotland in April).
In the second example, the big difference is in the appearance of the waves. These shots were taken at Jökulsárlón beach in south-east Iceland, in March 2012. The black volcanic sandy beach is littered with icebergs of different shapes and sizes that drift into the sea from the nearby lagoon, at the head of which is a calving glacier. The first shot is a 1/50th second exposure (pretty quick!) and the other is taken with the 6 stop ND filter (I think - I didn't write down which combination of filters I used for each shot) and is 3.2 seconds long. Personally, I think the 3.2 second exposure is much better, even though there's no impression of the strength or power of the waves. It just looks nicer to me.
Waterfalls are a prime subject for long exposures. At normal exposures the water is captured in motion (in fact to get a waterfall really sharp you need an incredibly fast shutter speed - not always possible if there's limited light otherwise). Slowed down just a little results in a nice smooth line of water. Again, whether you like it or not comes down in part to personal preference. This example is from Svartifoss, also in south-eastern Iceland, taken in March 2012. The first shot is 1/50th second exposure again and the second is 4 seconds long. I think I prefer the longer one, although actually I'm not completely sure on this one. This is why I always take some without the filters on, to ensure that I capture the shot firstly as I see it, and then with the creative twist, to see which one I prefer.
Long exposure doesn't work in every situation, especially if there are moving things, like tiny bits of ice floating, or trees moving, which can end up just looking messy. Sometimes this can work - reeds blowing in the wind look good, for example, but sometimes it doesn't. It's not a science, and that's another reason I like it - playing around with the different effects is interesting and fun and the results can be surprising.
There are a few things to bear in mind when taking long exposure shots that I thought I'd end with.
1) You must have a tripod, or something secure to rest your camera on. I also use either a remote shutter release or a 2-second timer delay. Any camera shake will blur the otherwise-sharp surroundings. You might also want to set the mirror lock-up, but I haven't found that this makes a difference.
2) Some filters produce a slight colour-cast. As you can see in the waterfall example there is a slightly pink hue. Sometimes with the B+W 10 stop this is extremely noticeable. I can usually correct this by adjusting the white balance, but sometimes it's quite difficult to get a realistic colour!
3) Always shoot in RAW, so that you can do the adjustments to white balance, exposure, etc.
4) If you've got stacked screw-in filters on a wide-angle lens, you probably won't be able to shoot at your widest, as the filters will show in the far corners. Try to buy filters that are as flat as possible (the B+W ones are fairly flat, but cheaper ones aren't!).
5) You may need to check the results for hot/dead pixels (during post-processing) and use a stamp/clone tool to remove any. These may be white or coloured. On my last camera - the Canon 60D - I had lots of these (white, blue and red), and the longer the exposure, the more I could see. It was also worse at higher aperture settings. I haven't done a great deal of long exposure work with my Canon 5D Mark III, but I'm hoping it won't be as bad, as it can be quite time-consuming to have to do this.
6) Make sure your sensor is clean. This is an obvious one, but I overlooked this before I went to Iceland last year. As a result, anything with an aperture of over about f/8 (ie. all my long exposure landscape shots!) will show any dust on the sensor as a round grey splodge on your shot. Again, mostly these can be removed using a stamp/clone tool, but it's a real pain. I had dozens of them on my shots from Iceland in 2011. It resulted in me researching about cleaning the sensor and investing some time and money in finding a solution (check out this article (point 10) for advice on this!).
7) Buy the best filters you can afford. They come in screw-in ones like the B+W, or square ones that need to be attached with a clamp. I went for the former option, mainly because I bought one round one and then didn't want to invest in a different system! Think about which might suit your way of working. The screw-in graduated ND filter is not ideal, as you cannot alter the place in which the dark ends and the clear begins - it's bang in the middle. You can twist it round easily, but if your sky's taking up 2/3 of the shot then part of it will be darkened but not all of it. With the clamp system then you can mount it at the right place according to where your horizon is. Some of the filters are seriously expensive (I think the B+W 10-stop was about £120), but they do vary from seller to seller, so it's worth shopping around. They come with varying different coatings, some of which are supposed to last better than others; this also affects the price quite dramatically.
8) Play around with a combination of different filters to get the right exposure length/aperture for the shot you're looking for. If you have screw-in ones and they get stuck, try rubber gloves to get them off (see this article for advice on this!).
9) As it gets darker you will need less glass and longer exposures. By dusk you probably won't need any filters, or maybe just a couple of stops, depending on the effect you're after (see image below, taken without a filter).
10) Use the bulb function if you need to take photos of longer than 30 seconds, and use a remote shutter release button.
11) Have a play around with different aperture/exposure length settings. I usually shoot in aperture priority (AV) mode, but if I'm doing long exposure shots I might use the time priorty mode (TV) or completely manual. Some people have produced tables about what settings you need to use, but I prefer trying a few out to see what I like. It can be quite time-consuming though.
12) Wrap up warm - it can take a long time to take these shots.
13) Go alone - taking long exposures is quite an anti-social habit. I now have to go on photography trips on my own ;)
14) Don't get completely carried away! Take some normal, filterless shots too. It's good to be able to compare the difference to see which you prefer. Plus it's far more sociable if you're with someone.
There's a great article by Peter Hill with loads more detail on ND filters, which helped me get the hang of it to start with - really worth having a look.
For more examples, have a look at the Long Exposure Gallery on my website. And let me know if you have any additional tips or comments!