Wow. Somehow in my interactions with LEOs over the years I seem to have avoided that sea.
The worst encounter I've ever had is a speeding ticket in a fairly blatant speed trap. Was it a trap? Sure. But I was still speeding. He was completely professional about it.
On the other hand, positive encounters:
I've had a LEO pick me up on the side of the road as I was hiking down the interstate away from my dead car. He gave me a lift to the next exit and made sure I was able to reach someone from a payphone (this was pre-cell days) before he left.
The LEO's who showed up for the 911 call when my wife died were compassionate and helpful. In hindsight, after the shock wore off, I can tell they scoped the situation out with some careful questions to make sure nothing illegal had taken place. Perfectly understandable.
Two ends of the seriousness spectrum there, but they've been typical of my encounters over the years.
Oh, wait. I do remember one horrible thing. I had to change a flat in the middle of a thunderstorm on the interstate in the middle of the night. The trooper pulled up and asked me if he could be of any assistance just as I was finishing up and putting stuff back in the trunk. Damn him, he should have come along 10 minutes earlier.