How about a car with a spherical tire? Now I know someone somewhere out there must have had this idea before but here is an idea of how it could work:
You use the design of a computer mouse but in reverse. I don't know if you remember the old mouses with the ball in them. The concept was pretty simple, when you moved the mouse, the little ball followed along in the direction of motion which then moved these little rollers on the sides of the ball that inturn turned the motion into information in the x and y axis (plural of axis?) and there by giving you the full range of motion on the plane. So my idea is the reverse of that. You have these two electrically controlled motorized rollers that move the cylindrical wheel.
Don't know if it would be better if they were parallel and perpendicular to the road or at 45 degree angles to it. I think it would be best if they were exactly at the sides of the sphere.
The sphere could "rest" on like three or more ball bearing type things. inside a spherical cage with the bottom of the sperere sticking out
Ideally you would have four of these to give you full range of motion. But you could go for a cheaper design by using one powered sphere and two dummy sheres that would not have rollers, would just roll in the direction of the leader.
A simple design would be good for road travel, offroading would be more complicated I think. The benefits of this kind of car are kind of obvious, don't you think? You could park sideways for one, and with properlly controled motion, one could simulate wheel driving. It has the best of wheel driving and the best of tank (tractor) driving in one design!
Reward: Oh, I don't know, how bout a cookie, ooh peanut butter, my fave! you know, whatever