Those of you into Rubik's Cubes may know about this guy; Oskar is a puzzle designer that makes crazy cool stuff on Youtube.
Here's his channel.
A few weeks ago he posted
this simple three piece transmission, with a reduction of 27:1. It works on a similar concept to
harmonic gearboxes. This seems like a design that might work for some mechanisms on the robots we build, particularly for something that needs a very large reduction and doesn't see a lot of torque. A similar design could probably be printed and interfaced to a motor quite easily, giving a cheap and quick gearbox for those teams with 3d printers.
If that's not enough,
here's a variation on that concept that goes up to 11,373,076:1.