Firstly, some chaps from Portugal's Guarda Nacional Republicana. Note lack of protective clothing, and you don't want to think what the rider's gun would do to his hip if he fell off. However, the strangest thing is that they are wearing spurs! He'll have to be careful that he doesn't burst his fire extinguisher!
Next is from the Volkspolizei (VoPo) of the old DDR. A Police bike based on a Simson Schwalbe moped. Probably OK for pottering around town, but a bit limited when it comes to a pursuing criminals in their high speed Trabant getaway cars!
Now a couple of cars from the US. Apparently, some Police forces are very strict on what you can eat at picnics!