Image stabilisation is very important to good photography with modern-day digital cameras for lenses ranging from telephoto down to wide angle. For film cameras, it used to be the domain of telephoto lenses. But a full frame film camera, unless it was using special high definition film, was effectively limited to 8 megapixels before graininess and other film characteristics showed. These days, people do not want these film characteristics to show through much as they are used to the cleaner images from digital photography. But 8 megapixels for a full frame camera for film has given way to 20 Mp digital sensors and the shake that using image stabilisation would solve for telephoto lenses now applies right down through to wide angle lenses.
There is a rule of thumb that is still in use for film cameras that was not true then and is less true now. That is to eliminate blur due to movement of the camera while taking a shot you should use a shutter speed that was the inverse for the focal length in millimetres so that for a 50mm lens use 1/50th of a second and for a 100mm lens use 1/100th of a second. Easy to remember but it was never true - although it is a good approximation for limiting ordinary motion blur for objects moving while you are taking a photo. Halving the shutter speed would have been more correct for eliminating actual camera shake such that for a 50mm lens use 1/100th second etc.. But now with higher pixel counts then a good guide would be to use the inverse of three times the focal length so that for a 50mm lens use 1/150th sec and for a 100mm lens use 1/300th sec etc.. You can experiment with this yourself. Assuming you have the stabilising effect of using a viewfinder and a reasonably good technique then you will rarely see camera shake at 1/150th for a 50mm lens but it will often be present at 1/50th sec.
If we use faster shutter speeds then less light enters the camera to fall on the sensor and so we have to use higher ISO speeds to compensate. Some cameras handle low light very well, like the Canon 6D, but the lower the ISO speed you can use, the better the results will be. At higher ISO speeds the image loses a lot of resolution and colour saturation that it would be better to keep (the image shifts towards an orange colour also, since this disguises noise that would show strongly in the blue region). The answer lies in having image stabilisation so not only can we use the old rule for film such as for a 50mm lens use 1/50th of a second shutter speed for a stable image but with good stabilisation. We might need less like 1/30th sec. This way we get more light hitting the sensor and can get a better image by using a lower ISO number but we have to be mindful of any natural motion of objects we are taking a photo of and if in doubt then stick to the old rule such as use a 50mm lens at 1/50th sec..