The following method can be used for reversing rotational direction without using simple gear train (in fact I hate gears as they are costly and require lubrication). I don't think that this method has (or will have) an application, but I expect it may be used in robotic applications where small torques are exist. This method is not going to use the conventional belts but it uses a belt which I call "double-V" belt. The following figures show how to do so.
And the belt is going to be like the following
And the belt is going to be like the following
