Gravity Probe B, a \$700 million NASA satellite experiment with gyroscopes controlled from Stanford University, an experiment that started more than 40 years ago (the oldest physics experiment alive) and that was designed to verify the effect of frame-dragging predicted by general relativity, is still unable to say Yes or No. Rotating Earth should "drag" the space around with it and transfer some angular momentum from the Earth to other objects.
The observed change of the axis of rotation of the gyroscopes can clearly measure the geodetic effect with the accuracy of 1% but the predicted frame-dragging - a general relativistic effect that is the closest reminder of the Mach principle, a flawed principle that motivated Einstein to find a new theory of gravity but one that was eventually refuted - is about twice as small as their current error margin.
They hope to get better results by the end of 2007: see press release.