Before VR, the rule of thumb was to use a shutter speed equal or faster to the length of your lens. So if you are using a 50mm lens, you'd want a shutter speed of at least 1/50 second or faster. If you are shooting with a 200mm lens, you'd want a shutter speed of at least 1/200 second or faster. With a DX body, you'd have to calculate the crop factor into the equation.
With VR, it allows slower shutter speeds to be used...sometimes up to 3-4 stops slower. If you don't use VR when hand holding and your shutter speeds are slow, you run the risk of having some blur in your photos from not holding the camera steady enough. You need to be aware of your shutter speed so you will know when to turn it on. Always keep it off when attaching and removing the lens from the camera. Keep it off when using a tripod. Use it if your shutter speed is slower than the length of your lens but providing your shutter speed isn't more than 3-4 stops slower. If it is more than 3-4 stops slower, consider using a tripod or change the camera's settings (ISO and/or aperture) so your shutter speed falls within an acceptable limit.