Harry Davis and me built a cable to connect a LEGO Power Functions (PF) motor to a Mindstorms EV3. The goal is to enable the EV3 to control PF motors. In particular I wanted to control a RC train motor through an EV3.
LEGO produced a cable (8528) to connect old motors (RCX) to the NXT, but it is no longer in production. You can still get them through Bricklink, but it will cost you dearly. You still need a PF extension cable to convert the old motor plug (RCX) to the current PF plug.
Firgelli produced a cable that allowed you to connect an modern PF to NXT directly, but it is also no longer in production.
There are two more solutions but both are more complex and costly. First, you can use the PF Mate from Mindsensors (currenlty $35). It sends IR signals to the IR PF receiver and thereby allows you to control motors even at a distance. The second option is the GlideWheel PF (currently $38) that directly connects a PF motor to the EV3. It also features a rotation sensor so that you can control the PF just like you would control a Mindstorms encoded motor. Both of these solutions offer a great functionality but they are also expensive, in particular since the components necessary for a custom made cable only costs a few cents.
At Amazon you can get a book Make: Lego and Arduino Projects: Projects for extending MINDSTORMS NXT with open-source electronics that will show you how to do such projects, but for now it is time to pull up our sleeves and do it ourselves. TechnicRobot already showed that it can be done but detailed instructions were not yet available. We also built a casing for our cable so that it can be easily integrated into your model. Here is the final result:
And here is a video that shows our solution at work:


