Why do we have to disable IS or VR when we use a tripod?
The common explanation is that the VR circuitry in the camera has a tendency to 'dither' when it doesn't have any vibration error to correct and so introduce its own errors. As D. Lambert says, some cameras have a tripod detect mode and can shut down VR or compensate when it senses that you're using a tripod.
Some high end telephoto lenses have a VR tripod mode that can correct for camera vibration caused by the mirror and shutter.
Of course, if your tripod is on a moving or vibrating platform you may get some benefit to leaving the VR turned on...
See a complete discussion of the ins and outs of (Nikon) VR at http://www.bythom.com/nikon-vr.htm
When you disable IS/VR on a tripod is probably the more appropriate question. Additionally, it may not necessarily be appropriate to disable it at all, and instead switch it to a different mode. As sensor resolution continues to increase, cameras are becoming more and more sensitive to smaller and smaller vibrations. Even the relative stability of a tripod with a very high resolution camera may still result in softening due to vibrations. The only two ways to combat that are to get a more sturdy tripod (such as the Systematic line from Gitzo), or to continue using IS even with a tripod.
Older IS mechanisms were pretty limited, possibly only offering 2-stop "generic" image stabilization. Modern IS mechanisms are much more advanced, usually modal, offering up to 4-stop improvements or more (prototypical Canon EF 800 f/5.6 L II lenses being tested in the field are purported to have 5-stop modal IS!!) A modern IS system on one of Canon's Mark II Telephoto lenses (300mm/400mm f/2.8 and 500mm/600mm f/4) have a 4-stop IS system with three modes.
Mode 1 is for full hand-held operation, stabilizing the image in both the horizontal and vertical axes. Mode 2 only eliminates vibration in the vertical, and is designed to support panning. Mode 3 is designed to only activate the IS system the moment the shutter button is pressed, and automatically detects the directions in which IS should be applied (horizontal, vertical, or both). It is designed for high action scenarios, and supports use with a tripod (generally with a gimbal type tripod head.) As a bird photographer, IS Mode 3 is pretty much the mode of choice, with or without a tripod.
If you have a lens with an advanced, very modern IS system with something akin to Canon's Mode 3 IS, you should trust the IS system to properly detect the situation and apply the correct type of stabilization automatically. Even when an intelligent IS mode is not available, many of the more recent IS/VR systems are "tripod-sensing", and will automatically detect the use of a tripod and either disable the stabilization system entirely, or change it's behavior to work better when mounted to a tripod.
IS systems work by moving a set of floating lenses.
When there is camera shake, the IS system moves the internal elements of the lens per micro-second in the opposite direction to cancel out the shakes.
Assuming you have a perfect tripod, there will never be any camera shake. However the IS system (more so for older lenses) may be too sensitive or poorly calibrated that it thinks there is some vibration it needs to cancel out.
So it moves the floating elements in the lens and creates blur.
However, like others have said, you probably don't have a perfect tripod. Even expensive and sturdy tripods cannot eliminate vibration 100% all the time. Especially when there is strong wind etc.
Modern IS system has also came a long way and the performance and reliability is constantly being improved.
So unless you are putting a lens with first generation IS on an extremely sturdy tripod, I would not worry too much about turning the IS off.