I've experimented a lot with transmissions. Here are a few of my inventions:

This is a bicycle-style derailer.

This is a drive splitter that uses a sliding worm gear. Reversing the motor switches the power path.

This is a two-speed transmission. Run the motor forward and you get low gear. Reverse it and you get high gear.

This is a planetary gear

For real power, here is a stepper motor driver. It runs the motor with speed proportional to the Lego motor speed.

This is how you pop apart a turntable to make a large gear. These are very useful in clocks.

Here is a list of Diagonal Beam Fittings

Here is a list of Gear Ratios