Yes, there is such a thing--it's not a prank you play on apprentice machinists. "Mike, could you go retrieve the square hole drill?" It turns out that a combination of a triangular cutter turning on an offset will actually cut a square. There's a demonstration here of how this works--apparently a practical application of pure math. This company sells a variant that produces a variety of polygonal shapes using this approach.
I have a request for a new ScopeRoller variant that requires me to cut a rectangular blind hole in acetal--and the more direct approach (using a small diameter end mill to square a round hole) doesn't produce a particularly attractive finish. I'm still mulling over some other way to accomplish the same ends.