I know a few people who carry around a dedicated light meter unit (such as this one by Sekonic) and use that to meter photos instead of using the meter built into their cameras (and these are relatively new mid-range DSLRs).
Is there any good reason why someone would do this?
The primary reason I can think of is to use it when scouting a location. You may not want to lug around all your gear initially, but you want to have a good idea of the ambient light.
This also would apply when you are doing a lot of lighting work, and you want to check the light levels as you go.
Getting the exposure right isn't easy with film, because there's no immediate feedback, so a light meter (intelligently used) is the way to go. With digital, a quick chimp at the histogram and blown highlight warnings, adjust, and you're ready to go. So no, I don't think it's valuable any more. In principle you could work without even a light meter in your camera if your estimation skills were reasonable and you were allowed to chimp once before every keeper.
All this talk of chimps and keepers makes me sound like I work at the zoo.
Although in camera light meters are reliable, and getting more so all the time, there is still room in your arsenal for the dedicated light meter.
I find I use mine most often when developing multi-light scenarios, mostly in portraits and real estate shots. The main reason is actually simplicity and speed. Once I settle on composition, I don't want to break it to use my spot meter in camera.
In other words I find it much easier and quicker to settle on DoF, then walk around scene once or twice checking levels on my subject with my dedicated. I can do the math in my head and come back to camera with a better sense of my scene. Then, any micro adjustments I need to do are through camera/master strobe unit. This, I think, works better than firing off a bunch of test flashes while your subject just sits there and you chimp away at the back of your camera.
That, and you look cool doing it too. That said, there's also no reason not to check your histogram before you settle on exposure.
Not only are light meters more versatile, you can do a few kinds of metering with them that you can't with cameras (and vice versa).
The meter you've linked (and I happen to own) has two kinds of metering: reflective and incident. Also, light meters can meter for flashes/strobes, something you can't do with modern DSLRs.
Reflective metering in the metering you know from DSLRs; light is reflected off your subject and back into the camera. While this kind of metering has many advantages: you can meter from far away, you take into account the whole scene, etc., it has many pitfalls. A scene with lots of snow or a dark wall can fool it. I'm sure you have a some images that are poorly exposed for no reason, among a series of well exposed images - that's what happens when a reflective meter is fooled.
Incident metering is a bit different; it allows you to measure the light falling onto a subject at the point of that subject. That gives you a "truer" exposure, one where dark material will come out dark and light material will come out white. Sekonic has a pretty good FAQ entry on the subject. When shooting people, you would measure at the subject's face with the dome pointing at your lens, something you often see in movies.
With a modern flash meter, you can also meter flashes and strobes. The meter you linked can either be hooked up to a PC sync cable, or can be set to react to a flash of light. This lets you measure the results of strobes you've set up without using a digital camera or a polaroid. It also lets you check that you have nailed your exposure, without checking your LCD a thousand times.
In addition to measuring the whole scene, with incident metering, you can measure the light from each of your strobes, and if you ever look at strobe notations, that's how they're usually recorded. This you measure at the subject, pointing the white dome at your various lights while firing them off separately. This lets you quickly jot down your flash ratios, and that's extremely useful when recreating a look.
Oh, and the reason I often carry that Sekonic meter around: It's much, much smaller than my DSLR and I use it for my film cameras that don't meter.
Cameras tell you what you they think you want to know. Light meters tell you exactly what you NEED to know to make a great exposure.
The camera's sole decision logic is based on reflectivity of the subject. It can only 'guess' as to how reflective your subject is. Conversely, a handheld meter measures, with impressive accuracy, the light falling on the subject regardless of it's reflectivity.
Hence, the meter is telling you what you "need to know" (actual light) VS guessing.
Even if you are using your handheld meter in a 'reflective' or spot metering mode, you're making the final decision regarding a subject's actual reflectivity.
I've used Sekonic meters for nearly 15 years as a commercial photographer. Best metering device in my book. I don't leave home without a meter, it was the single smartest purchase in helping me diagnose my exposure errors.
Also, one excellent side benefit to using a handheld meter is you will begin to calibrate your eye to the light available in a scene. Soon, you will be able to walk into a scenario and just about nail the exposure without having to meter. Knowing how much light is available to a scene is a first step in getting a great shot. Everything is based on light.
Incident meters tell you about the light falling on the subject.
Reflective meters (like those built into cameras) tell you about the light reflected from the subject.
As you can imagine, reflected light depends on (a) nature of the incident light and (b) reflective properties of your subject.
Since the reflective meter does not know what the subject it, it makes some assumptions about it. These work, most of the time. However, low-contrast dark or bright scenes give reflective meters trouble, because they break the built-in assumptions.
For outdoor (ambient) lighting, an incident meter is not very useful. With your camera's meter and a good understanding of what information it is (or isn't) providing you, you can easily get the exposure you want.
Incident meters are most useful when you are using flash, or a combination of flash and ambient. Some of the more sophisticated ones calculate the ratio of flash-to-ambient to make keyshifting easier.
All of the existing answers that were written back when this question was asked were accurate at the time that they were written. But since that time in-camera metering has improved dramatically. The introduction of RGB and RGB+IR light meters and the processing that uses the information collected from such meters to calculate exposure has improved the accuracy of in-camera reflective light meters under a wide variety of 'non-typical' lighting scenarios considerably.
It is still true that in-camera meters measure only reflected light. What has changed is how well they measure that reflected light and how well the light they measure is interpreted.
With the ability to distinguish color and to see higher resolution differences between various areas of the frame has come the ability to recognize the scene as closely matching an extensive library of different scenes included in the camera's firmware. Single element monochromatic light meters, or even those with a few discrete elements, could not tell the difference between many different types of scenes.
But cameras with higher resolution color metering and the logic to use that information now can.
The new wave of cameras with RGB meters can tell the difference between a white dress and a black tuxedo, or the difference between a beige dress and a blue dress under poor lighting conditions (heh heh), or the difference between a black cat in a coal mine and a white cat in the snow.
Incident metering that measures the light falling on a subject is still the most accurate way to meter a scene. But reflected light meters that can distinguish colors and patterns have closed the gap considerably.