Here's a cool application for a PID:
I have a PID controlling my HLT heating element. The HLT has a builtin HERMS coil. I'm recirculating wort from the MT through the HERMS coil. My temp sensor is reading the return wort temperature back into the MT, and is adjusting the HLT heating element temp accordingly to maintain an exact 150F wort temp.
With the above example, I don't care what the water temp is in the HLT, I'm only concerned with the wort temp returning back into the mash.
That would be very hard or impossible to do with a regular temp controller.