I've had crazy neighbors and I've been the crazy neighbors.
When I lived with my parents there were these people that lived down the street from us that loved to complain. Most of their complaints were directed at the amusement park that our properties backed up to. They were constantly upset about the noise of the place. The amusement park was there well before their house was built though, so they really didn't have a leg to stand on. Despite this, they called many community meetings to complain about it. They even took the owners of the amusement park to court over it saying that the loud music and children screaming had ruined their sex life.
In addition to complaining about the amusement park, they called the cops every time anyone in the neighborhood had a party. I had one where we were having a live band playing, so before even planning it I went around to all of my neighbors and asked if this would be an imposition. I also invited all the neighbors to the party. They all said it was fine, and some of them came, but these people called the cops on us even though they agreed that the party with the loud music would be okay. The cops stayed to listen to the music for a little while. It was lots of fun.