How do you connect a router to another router? The ethernet cable connection has to be a crossover cable (Type A on one side, Type B on the other) to connect inputs to outputs and vice versa. You'd have to verify which type is currently being used, either cut off one of the heads and redo it opposite, or in the case of a jack, just repunch.
Why would you do this? You might want to extend the range of a wireless router by placing another wireless router at the end of an ethernet cable. This cable, as mentioned above must be type A on one side and type B on the other, also known as a crossover cable.