Anti-shake (Konica-Minolta), image stabilization (Kodak), optical image stabilizer (Canon) vibration reduction (Nikon), shake reduction (Pentax) , mega optical image stabilizer (Panasonic) and super-steady shot (Sony) are all technologies designed to reduce camera shake. These technologies are extremely valuable for shooting when insufficient light is available.
Stabilization technology allows shooting at shutter-speeds 2 or 3 stop slower than normally expected. The expected rule is to shoot at 1 over the focal-length of the lens or faster. For digital cameras, the focal-length multiplier must be applied here too. Lets say we have a 24-70 lens mounted on a DLSR with 1.5 FLM (Focal-Length-Multiplier) At the wide end, the effective focal length is 36mm. This means that a speed of 1/36 or faster is required, commonly 1/50. At the telephoto end, the effective focal length is 105. Thus, a speed faster than 1/105, commonly 1/125 is required. With stabilization, effective of 2 stops, the 1/36 required would become 1/9, commonly 1/10. At the telephoto end, the required 1/105 would become 1/26, commonly 1/30. For a 300mm telephoto end, equivalent to 450mm, 1/450 would be required without stabilization, and 1/112, commonly 1/125, would be required with 2 stops of stabilization.
It is important to know that stabilization is a best-effort technology and does not guarantee its effectiveness. Some people shake more than others, making it less effective. Another way to increase potential image sharpness is to increase the ISO sensitivity.
For each ISO stop increased, a camera is guaranteed to require 1 stop less light to achieve the same shutter-speed. This is the opposite as stabilization which allows slower shutter-speeds. The major difference is that anti-shake reduces the effect of camera movements only. Increased ISO reduces the effect of camera movement and subject-movement. For this reason, only an increase of ISO is effective when shooting action in low-light or with a telephoto lens.
With digital cameras, just like with film cameras, an increased in ISO reduces image quality by introducing noise which causes loss of details. Higher-end cameras introduce less noise, so there is a point up to which it is acceptable to increase ISO sensitivity. This point is highly dependent on the camera. As a general rule, larger sensors show less noise at higher ISO.
In summary, stabilization is immensely valuable unless shooting subjects in motion. In such cases, the ISO sensitivity must be increased. Due to noise, stabilization is preferable over increased ISO sensitivity when both can be applied. In case when stabilization is insufficient, one can also increase the ISO. This also highlights the value of cameras with less noise at high-ISO sensitivities.