There are two ways to reduce the base of native ISO (the lowest setting possible on the camera). One is to make the sensor less efficient, so that the less of the incoming light is captured. It is easy to see how this reduces the sensitivity. However, as already stated in other answers, this would only be of use to the minority people who regularly find that they have too much light whereas the majority of photographers struggle with not enough light for the most part!
However there is another way to reduce the base ISO and that is to increase the capacity of each pixel (referred to as the well depth) so that it can store more charge (and hence more light) before becoming saturated. This method does have a genuine advantage at all sensitivities.
It is a little trickier to see how this affects the base ISO, however you have to remember that whatever readings the sensor takes eventually get mapped to the range 0-255 either by the camera or a person during raw conversion (or 0-65536 for 16 bit images). Imagine two sensors A and B, A has twice the capacity per pixel. When you shoot an image with A at 1/30s shutter speed the highlights are just about to clip. Now when you use B, you have to use 1/60s because of the decreased capacity - if you used 1/30s you would overexpose the image.
Whatever values the sensors record at the saturation point they still get mapped to 255 so will look the same. Given that with B you get the same image but with half the exposure time (all else being equal) this means B has higher sensitivity. If the base sensitivity of camera B is ISO100 then the base sensitivity of A is ISO50.
The point of all this is that if you can reduce the base ISO by increasing pixel capacity then this is a good thing as it allows you to have lower noise and greater dynamic range. To understand why this is the case, you first have to let go of the idea that increasing the ISO setting increases noise, it's simply not true, here's an answer I wrote on the subject: What is "ISO" on a digital camera?
The short version is that noise is mainly caused by lack of light (the less light you have the more random variations in photon emission show up in the image, see http://en.wikipedia.org/wiki/Shot_noise) it just happens that if you increase the ISO setting of your camera other settings have to change which result in you getting less light and more shot noise. It's the lack of light that produces the noise, not the act of amplifying the signal.
So even though we have to use amplification to get ISO100 out of camera A, we let in the same amount of light as camera B shooting at ISO100 and thus can expect the same level of noise! So camera A is no worse, however we do have the option of going to ISO50, letting in more light and thus getting less shot noise!
We also have the option of using ISO50 but with the same camera settings as B is using to shoot at ISO100, we let in the same amount of light so can expect the same level of noise, but if the scene suddenly gets brighter B with clip the signal whereas A will carry on with it's extra well depth, thus having higher dynamic range.
These examples are a simplification, there are other sources of noise, but in general having a "less sensitive" sensor can be a good thing. It is difficult to engineer deeper electron wells however, which is why you don't see cameras go below ISO50. You do see differences in well depth though, for example the lowest ISO available to the 35mm sensor Canon 5D is ISO50 whereas the same generation APS-C sensor in the Canon 30D the lowest ISO is 100 this is due to the extra capacity in the larger pixels of the 5D.