I had a cop pull me over for making an illegal right turn, and the reason he started following me, was for leaving a place he didn't want me to be at.
Basically. I was looking for a good place to watch a meteor shower, and pulled into this parking lot outside of a state park, which was not trespassing or anything. It was open to the public, and it was early enough in the day to not be a problem. He was there, radaring people on the nearby main artery road. I got out of my car, walked to one of the sitting spots that I thought would work, and realized it wouldn't, because the direction of sky I needed to see, was obscured by tree cover. So, I left, as I was moving back to my car, I see him pull out onto the road, which I figured was him going after a speeder. I leave, and head out for some other spot. I do in fact make an illegal right turn, because my turning signal was broken in that car. As he's giving me the ticket, he explains that he went to the other side of the road to watch me, because "he didn't like that I pulled into the place, they don't like people showing up there at that time of day. And the fact that I left shortly after getting there was suspicious." So I replied "So, let me get this straight, you decided to follow me, because I left a place you didn't want me to be at in the first place?" He kind of paused for a second while he worked out the idiocy of that and said "Yes." To which I just shook my head and said "Ok man, whatever."
Another time, I was on a date with a girl, and we had about an hour or so to kill before going to see a late movie. Again, there was this public park (different one) that I took her too. We were going to swing on the swings, and basically just get to know each other and talk while we waited for the time to go to the movie. As soon as we pull up, I see flashing lights in my mirror. I get out of the car, something we were doing anyway, and see two cops approaching me from behind. I look at them and say "What's the problem officers?" They look at me and one actually says. "What do you mean?" I open my arms, and gesture to the completely empty parking lot, except for my car, and their flashing lights, and blocking my car in so I couldn't leave. Indicating "who else would you be hear about but me?" I repeat. "What's the problem?" They proceed to come up to me and say something about "The local residents have reported problems of young people coming here at night and doing things they shouldn't...." heavily implying I was there to do the same. I reply with "Ok....and?" They seem perplexed by my response, so they repeat it basically. "People come here and do things they shouldn't..." and I respond with something like "Ok well, we just got here, as you know, since you followed me into the parking lot....is the park closed to the public at this time?" Which I knew it wasn't, it stayed open until like 10:30pm, which I thought was oddly late, but hey it was officially posted, and it was only like 8:30 when this happened. The two cops looked bothered that I was aware of the laws about the park and said "No...no it's still open to the public." And I said something along the lines of "Ok well, we're going to go hang out in the park then, goodnight." And I turned and walked away, ignoring the cops completely at that point. We went and hung out on the swings, talking and getting to know each other, and the girl said "I can't believe that happened. I've never ran into the cops and not had something bad happen."