Do routers prioritize control traffic?

I know routers today have the ability to prioritize traffic, but last I heard, these controls are not often used for user traffic (let's not discuss net neutrality here). Are they used for control (e.g., routing) traffic? Please say a bit more than "It depends!" :-) Our students are interested in real-world practices. Answers on or off list are welcome. Christos Papadopoulos Colorado State University.