We've definitely come across some strange robots over the years designed to perform all sorts of interesting and unusual tasks.
However, one of the most unusual robots I've seen was built by a company knowns as BeatBots. The robot you see below doesn't actually have an official name - and seems to be executing a complex task in an effort to achieve something very simple.
The sole purpose of the robot? To drag a dry erase marker along a white surface on the wall. The robot itself has a solenoid that presses the dry erase marker to the surface - so it's capable of moving back and forth, and up and down on the wall, all by hanging from wires.
The wires you see in the video provide the robot with the required power and stability to operate. It doesn't appear that the robot has the programming to make complicated shapes, but it can draw straight lines and approximate curved lines, at least from what I can infer from watching the video.
Currently, the brain of the little robot is powered by an Arduino controller. To be perfectly fair, the robot is only in an early stage of development, so who knows what the final product might look like and what it may be end up being used for.
Personally, I don't see a practical use at this point in time. However, if you could design a robot like this that was capable of cleaning windows or mirrors without needing wires for power or mobility, well that would be quite impressive indeed.