Why 8s or 30s?

Longer exposure allow you to:

• get more light to reach the captor (night, etc)
• have nice blurry effects (waterfalls, etc) (in that case, usually you need a dark ND filter to compensate, so that during that long exposure you don't overexpose). For exemple: photograph of buildings, using the maximum ND filter available, will make people/cars "disappear", sometimes "completely".
• On the downside it will probably also induce more noise. For this, most pro cameras, and some (many?) non-pro too, offer some kind of "long exposure noise reduction" to compensate, offering a great reduction but it can't be 'magic'. This feature usually work by taking, after the picture, another picture with the shutter closed (a "dark frame") and with the same exposure time. That 2nd picture will be used internally to find where the noise builds up. Then the first picture is corrected using that data. But it does take twice as long (so you have to wait to take the next picture...)

Shorter exposure will allow you to:

• Limit movements (those clouds in the background will stay sharper, because they moved less)
• have a different blur effect (waterfalls, etc)
• keep noise in check
• save some time! (maybe those shorter 8s can help you setup the longer ones, but you'll need to compute the new exposure parameters to compensate for the time difference)

A camera that offers a 30s max exposure time limit will also be able to do shorter ones, but the opposite is of course not true (as the limit, by definition, limits the exposure time offered by the camera). That limit on exposure time is actually the limit time the camera allows itself to open for. If you use Tv mode, you'll only be able to go that long. If Av mode, it can only go up to that limit to compensate the exposure, etc. (At the opposite on the time scale, there is also a minimum time, which depends havily on the camera build).

However, you can often also "bypass" the long-exposure limit : some cameras offer another mode where you tell it when to close the shutter, either by pressing another time, or by holding the button pressed (and the shutter opened) until the end of the exposure time you want. [The latter is called B or Bulb mode, on Canon EOS 5d mark ii, for example]. This allows for even greater exposure times (and I don't really know its limitation, apart from noise buildup, the risk the captor may suffer if the subject is bright, the battery life which you'll need in order to save the final picture, and movements of the subject(s), or of unwanted things passing by during those long exposures... And, if not using a remote control, your own ability to keep the button pressed, if your camera is using the "keep shutter open until depressed" mode).

(interrestingly, on the short-exposure limit side: you shouldn't be able to bypass this limit, as it depends on the camera shutter speed, etc. But in some cases, you can cheat that by using specialized very-short burst flashes, and a low light environment, having your subject only illuminated for the flash duration... Sometime used to photograph water drops, bullets going through something, etc)

There is probably many more to add in each, I'll update if I can (or maybe someone will do one of those 1200+ point answer instead ^^)