There is no reason I know of that using an image stabilised lens on a tripod should damage the lens. It is, however, counterproductive as the tripod itself is already stable and any movements you make with the tripod will be fought by the image stabilization.
If you try to move the camera while it is on the tripod, the IS will slow down how fast the lens actually follows your movement and this lag is undesirable, thus when using a tripod, you should turn off the IS.
Additionally, looking at the B&H page that rfusca found, it appears that the concern being described is a lesser (but minorly possible) concern that the rotation of the gyroscope could induce shaking in the lens element when the camera itself is well secured.
Basically, the thought process is that if the camera body is unable to move at all, then the rotation of the gyroscope, if slightly off balance, could start to cause the image stabilizing element to begin to wobble in sync with the rotation of the gyroscope. Each additional rotation would add a little more strength to the movement of the stabilizing element since the camera body can't absorb the energy being released by the gyroscope.
For this to happen though, the system would have to be amazingly stable and you would notice it from an obvious and growing wobble in the image as you looked through the viewfinder or looked at the LCD screen.
In more complex IS systems it may also be possible that attempts to correct will continue to cause more corrections, but again, this would still show up as increasing amounts of vibration in your viewfinder.
Point is, turn off the IS on a tripod, but it's not going to damage your camera without you being able to notice a problem growing and is unlikely to be a serious problem even then. It may be theoretically possible, but actual practical and common problems still make it worth turning off.