Ballbot I've been waiting for.

Somehow I couldn't figure out myself how this could work, but I have anticipated the coming of balls instead of wheels for a while.

Ballbot built by Ralph Hollis, director of Microdynamic Systems Laboratory can balance dynamically while moving omnidirectionally on most surfaces.
"Mobile robots that locomote with wheeled drives are slow and awkward, with wide bases providing static stability. What is needed is an entirely different approach to locomotion: mobile robots that are safe; dynamically agile and capable of graceful motion; slender enough to easily maneuver in cluttered, peopled environments; and which readily yield when pushed around. Intelligent machines of this sort can only be achieved with dynamic stability."

Video of response to a disturbance and Video of point-to-point motion.

(via)