Prior to VR, the rule of thumb used to be you can shoot without a tripod when the shutter speed is at least the same as the focal length. What I mean is if you are shooting a 50mm lens, then you would want to hand hold the camera at 1/50 second or faster. Now with VR, you are supposed to be able to go up to 4 stops slower shutter speed than the focal length. Personally I'd use a tripod if at 4 stops under.
Here's an example: If shooting a 50mm lens with anything less than 1/50 sec shutter speed, then add VR if your shutter speed is anywhere from 1/30, 1/15, 1/8, and possibly 1/4 sec. If slower than that, use a tripod. When using longer lenses, the same thing applies. When shooting a 200mm lens, shutter speeds of 1/200 sec or faster is fine without VR. Use the VR for 1/25, 1/60, 1/30, and possibly 1/15.
EDIT: When using a DX camera, you may want to consider the 1.5 crop factor into the equation. That means if at 3 or 4 stops under, you may want to use a tripod instead of relying on VR.