Q:

Why is the lowest ISO always 100?

The lowest ISO on digital cameras always seems to be 100. It would sometimes be useful to have much lower ISOs, mainly for long exposure photography.
What isn't there any 50, 20, or even 10 ISO setting ... ?

A:

Camera sensors (see this article for an overview) consist of a very large number of individual sensor elements, each of which can be regarded as a bucket that collects photons. These buckets have a maximum number of photons they can capture before they become full, which is called being saturated (this is when the highlights clip). This maximum capacity is not affected by the ISO setting of the camera.
As stated in this question the lowest or "base" ISO usually corresponds to the unamplified sensitivity of the sensor, increasing the ISO results in the readings from the sensor being multiplied, meaning that the maximum value that can be stored in a recorded image can be reached before the sensor wells become saturated.
Decreasing the ISO would therefore require a 'deamplification' of the sensor readings, which can only be done after reading the sensor levels and so cannot actually decrease the sensitivity of the sensor to incoming light. This will cause any artificial decrease in sensitivity to also result in a corresponding decrease in dynamic range as you are compressing the total range of sensor levels into a less-than-total part of the range of levels that can be recorded in an image.
All this is a long way of saying that camera sensors have a fixed minimum sensitivity to light, regardless of what ISO it is referred to as. Any artificial decrease of ISO below this sensor minimum will both not actually make the sensor less sensitive to light and will also decrease the range of light levels that can be recorded in an image.
Neutral density filters solve the problem of wanting a longer exposure (without clipping) than the camera's minimum sensitivity allows by reducing the amount of light that hits the sensor, which causes the sensor buckets to fill up at a slower rate than they would without the filter being used.
Decreasing the ISO below the minimum can only be done after the recorded values are read from the sensor and therefore cannot actually darken the image hitting the sensor which is what is required to get a 'genuinely' extended exposure time. What such a decrease would result in is an increase in perceived exposure time when looking at the final image that is actually just an artefact of squashing the light levels recorded on the sensor into a smaller range when writing them into the image. Neutral density filters do make the image hitting the sensor darker which does result in an extended 'genuine' exposure time.
The numerical value of the lowest ISO is calculated by reference to standards as described in this question.

A:

I can't find a reference now, but I remember once reading that sensors have a usable range so the lowest ISO is chosen in a way to make the most useful range. My camera's native range is ISO 200-3200, which is five stops. If that were to start at ISO 50 I'd be thrilled to have such a slow speed available when I want/need it, but five stops would mean the highest ISO offered would be 800 -- and I shoot far too much at 1600 and 3200 to want to limit myself on the high end. Plus, ISO 800 would have much more noise -- perhaps like ISO 3200's noise level. Starting at ISO 10, that means the upper limit is only 160. 200-3200 makes for a much more useful range than 50-800 or 10-160 for most users. It's easy to add a neutral density filter to get slower shutter speeds, but there's no "brightening filter" to negate high ISO requirements. (But wouldn't that be awesome?)

A:

This blog post on DPreview indicates that:

ISO 100 is the "normal" setting for most cameras, although some go as low as ISO 50.

However, it doesn't indicate why this is or which cameras have this setting.
This post on Digicaminfo has the following statements:

Most DSLR's produce essentially noise-free images at their lowest ISO speed settings, usually ISO 100-200
Small sensor digicams by comparison tend only to be able to produce low noise images at their very lowest ISO speed setting, usually ISO 50/80/100

Which would indicate that having a lower ISO setting than 100 wouldn't actually produce a better image because you can't have less noise than "noise-free". Manufacturers have apparently made this decision, presumably based on research(?), given that there are other ways (neutral density filters, for example) of reducing light levels.

