The Kilogram is the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units and 17 derived units in the SI system are defined relative to the kilogram, so its stability is important.
To maintain its stability, several projects have started, trying to tie the measure of mass to universal constants. This video shows one of the most promising development, the Watt balance method.
More info about the Kilogram on Wikipedia.