Should I drink protein powder on days I don't workout?

It can depend! Everyone needs a certain amount of quality protein in their diet, even on days you aren't working out. In fact, your body recovers a lot of your rest days, so your nutrition is essential on those days as well. 

Some people choose to only consume their protein powder on days that they workout, and if you would like to do that, then that's completely okay. Just make sure that you are still meeting your protein needs on your rest days by eating enough protein foods. Your protein intake should come from a combination of different sources in your diet.