Can anyone offer any tips on achieving long exposures (with the intention of blurring water, clouds etc)?
Stable Tripod is a must if you want to be able to compose.
If you want exposures over 30 seconds, use Bulb mode, as most of the cameras only meter up to 30 seconds.
Use small apertures, low ISO and add ND filters if there is too much light. You probably want your sensor to be clean also as small apertures will render the dust relatively sharply.
Use remote trigger or self-timer so you don't touch the camera during exposure.
It's better to use mirror-lockup to avoid camera shake caused by mirror movement.
Disable all automatic features, like auto-ISO, auto-flash, probably also autofocus (just focus once from a contrasty point and then switch to manual).
Most of the cameras have something called "long exposure noise reduction" which will double your exposure time, expose a dark frame and subtract it from the main frame to lessen noise. If you're OK with the exposure time doubling, use it, otherwise disable.
When the exposures get really long (up to and over 30 min) you might want to do it with fresh battery. Around these times amplifier noise will probably be problem with digital cameras - it will result purple glow in some parts of the frame.
Should you be doing it with film, keep the reciprocity failure in mind. You can check the needed exposure correction amounts from the film manufacturer's website.
The "long exposures" starting from anything that is not hand holdable any more are usually used to add dynamics to the picture. Motion blur can sometimes result very nice photos, it just needs a lot of experimentation to get right.
The long exposures ranging around 1-30 seconds can be used to play with the balancing lights concept. The prime examples of balancing light work are the photos taken at after dusk or pre-dawn, when there is some natural ambient light available, but it balances well with the artificial light sources.
You can also balance ambient light with flash or other kinds of controlled artificial lightning. Experiment with different directions and vary the intensity.
Here is an example of balancing light concept: photo with natural light only and the same shot with additional artificial lightning (this is the winner of "Astronomy Photographer of the Year 2010").
In contrast the very long exposures are usually used smooth out any movement and create a static and mysterious mood instead. Good examples this approach can be found among Michael Levin's works.
In addition to the in-camera methods (small apertures, low ISO, ND filters...) you could take several exposures, and average them digitally in post-processing. That should work well for things like waterfalls and streams, but could introduce gaps in star trails, automobile traffic, etc.
You could use a Tripod and also a remote trigger (self-timer is also ok). But in day light I think 2 major components
Also the use of ND filters considerably help the process. Incase of emergency you could even use your sunglasses. But be careful that it cover the whole lens.
Also if the scene allows it use the extended zoom. You get couple of extra f-stops with that.
A couple of people have already mentioned ND filters. An alternative is to stack two polarizers and "cross" them (make sure the front one is not a circular polarizer though) to reduce light transmission. This can be particularly effective when you need a really long exposure (e.g., to get a 10 minute exposure in broad daylight to make tourists "disappear").
The other two answers cover most of it, but don't forget to set the ISO to as low a value as possible - 100 at most. This will allow you to have a longer exposure.
In general, use a smaller aperture. If that will not give you slow enough shutter speeds, neutral density filters (ND-filters) will give you slower shutter speeds without altering colors and such in the scene. They come in different strengths and can be combined. If you go shopping for an ND filter, make sure not to mix up graduated ND-filters with regular ones. The graduated filters have another purpose.
Another option is to use a polarizer (which will typically steal 2 stops worth of light).