Here is an interesting diagram I found on the Canon Europe website:
It shows the advantages and disadvantages of in-body stabilization versus in-lens stabilization.
IBIS is very effective for shorter focal lengths, but not all that good for longer ones. In-lens stabilization is great for longer focal lengths, but is far less effective for shorter focal lenses.
If you have a camera body and lens with built in stabilization (and your camera supports both modes at the same time), the "Cooperative" stabilization works best. That being said, good camera technique and a forgiving wider focal length means that a camera body without IBIS will still result in sharp images.