There is one rule about the speed and focal length. To avoid camera shake i.e. blurry photos you should use shutter speed = 1/focal length. Let suppose you use 300 mm so your speed should be at least 1/300s.
With image stabilization you get possibility to shoot with slower speed. For example if your lens have 3 stops stabilization you can shoot (from example above) with 1/300/2/2/2=1/37s (the speeds are just example)
P.S. Of course the above rule depend of how stable you can handle your camera. I personaly have some photos, created at 1/8s (w/o IS) which are in focus, w/o any blur. From other side have other photos at 1/100s (with IS) which have motion blur :)