I don't have any particularly exciting cop stories...
When I was a kid (11?) I was fishing in a creek on someone's else' property when an officer came over, having been called by a busybody I assume... he told us we had to leave and then advised us to hide next time we see someone coming, so that he wouldn't have to tell two harmless kids they're not allowed to fish in a creek in the middle of nowhere.
A few years later, still a minor I was walking home from a nearby town (it's 10 miles, we were homesteaders, my ride fell through) and might have smelled like something illegal, an officer stopped me as I walked along the road, sized me up and dropped me off at my house without even waking up my parents.
A bunch of years later I was working at a software company and after a long and not so good day at work I might have pushed my gas pedal down a bit farther than was prudent while leaving my company's parking lot, depositing a single line of rubber particles along the street to much noise and satisfaction, only to be greeted by flashing lights in my rear view mirror from an officer I didn't adequately notice previously. He could see that I was having a tough day and advised me to tough it out just a bit longer in the future, wait till I got home and then have a beer or something instead of attracting attention from police.
More recently I was driving in medium dense traffic in Southern California, pulling a small U-haul enclosed trailer in the center lane of a 5 lane freeway and getting passed continually by F250's pulling open trailers full of sand rails and quads and dirt bikes etc, I was going 68mph, they were all going 70-90mph, traffic in general was going 70-90mph and of course California's highway speed limit for anything pulling a trailer is 55mph. I'm a part time commercial truck driver and quite familiar with this fact, but also figured that staying with traffic is safer than being the actual slowest thing on the freeway. The officer then proceeded to fill my mirrors with as many bright and flashy lights and demand that I change lanes and pull over to the side of this busy freeway while blind, before he gave me a huge lecture on safety. In my mind I tried to telekinetically give him colon cancer. That was a $460 ticket for um... I guess for having a smaller trailer and going slower than all the hundreds of other trailer-towing speeders he didn't pull over? Fuck that guy.
And most recently a police officer let me marry his sister, not that he had any say in the matter but at least he didn't try to stop it so he's OK in my book.