I have a fairly simple idea for a new kind of wheel that I will describe to you now. It's not really possible to build a very good one with today's technology, but it seems as if it could be possible with more advanced fullerene-based robotics.
I got the idea for this wheel while reading about Usain Bolt and the possible limits of human speed. One of the obvious factors that determines speed is the total amount of force applied to the ground per time interval. Humans and other animals with legs can only contact the ground as many times as they have legs per running cycle, limiting the amount of force they can apply.
The classic workaround to this limitation is the wheel, which can apply constant force to the ground as long as its power source holds out. Of course, the wheel has its weaknesses. A wheel can't operate efficiently over uneven ground, and can't scale certain obstacles. The solution is to create a "wheel" that consists of a bundle of tentacles, or "whiskers" which can lock together, become rigid, and behave like a solid wheel while moving over flat ground, but can unlock and independently articulate when moving over rougher terrain.
This concept takes the strengths of the wheel and bipedal/quadrupedal/tentacle locomotion and merges them into a single system. The idea wouldn't work too well with present-day robotics because 1) the fine coordination and control required between the whiskers to merge into a wheel or detach from one another and articulate smoothly over uneven terrain would be a huge challenge by current standards, 2) miniaturization and nanotechnology has not yet advanced to the point where a thin, strong tendril or whisker can quickly be changed from flexible to rigid in a fraction of a second (magnets are not good enough, it needs to be mechanical), 3) the idea works best when the power-to-weight ratio of engines can be improved beyond today's current standards, and when engines can be made small enough to be installed into the whiskers themselves.
If all these requirements were met, however, you'd have quite a system. Locomotion based on tentacles alone would be very effective for scrambling over rough terrain, locomotion based on wheels alone would be good for the highway, but what if I need both? The whiskerwheel can adjust to be more wheel-like or more tentacle-like based on the demands of the moment. Nano-cilia and lubricants could be used to keep the interfaces between the whiskers clean so they slide past each other fluidly when necessary. The whisker format would also allow the wheel to increase the surface area of its contact with the ground beyond a typical wheel fitting in the same space, improving traction and increasing the total amount of force applied to the ground, increasing speed.
You could even build a robotic system that simply is a whiskerwheel, rather than using a whiskerwheel with a conventional axle-based mounting. A system like that would be a sort of robotic shoggoth.