At one point, when DD#1 was little and the only kid, I was driving some sporty monster whose make escapes me, but you couldn't see in the back seat from outside. I used to drive the commute lane on part of my route to the baby sitter in the morning, and for a week or two, I think I got stopped EVERY morning, only to have the cop come up and see her there in her car seat, apologize to me, and go back to his car. After a week or two I think they must have learned and put out the word, and it no longer happened.
The scariest thing I've ever had happen with a cop car was driving down a lovely local freeway, in a lovely local town, on a 50 mile trip back to my apartment, when an unmarked car came up behind me, landed and stuck to my rear bumper, and both sounded his siren and flashed his little mobile light at me. Scared the *%^)*(& out of me. He had plenty of room to go around me on the right (multi lanes, perfectly legal) but he wanted ME to move over. So, I moved, and he zipped on by, and about a mile down the road, I saw him parked at the off ramp, doing exactly nothing.
The second scariest was one morning when I was groggily going out for donuts really early, and came to a stop at a 4 way intersection. And it's a damned good thing I did so, because a cop coming the other way ran his stop sign and would have T-boned me if I hadn't stopped properly.
But, to give credit where credit is due, one memorable date, late at night, the cops took me home and lectured me about how they were going to have to talk to my mother when we got there (because my date had done a hit and run, and WHY I hadn't peed my pants is a mystery to me) and after thoroughly cowing me, as soon as I put my key in the lock, he turned and walked way. I turned and asked him,"Wait! Didn't you want to talk to my mother?!" I don't think he even answered me, he just left! I'd have baked him cookies the next week if I'd know who he was and were to take them.