Soon after I had graduated from college (so around 1986), two police officers banged on my apartment door about 4:30 am. Apparently, someone had told his girlfriend that he was committing suicide and gave them my phone number as where he was. I don't know if he gave the wrong number or if it was misheard or what. We talked through the door for a few minutes assuring them that I was safe and alone, but then they had to come in and check the place. I had been asleep and was still in my pajamas and was newly living alone, so it was a scary experience. Also, I worried a long time about the person.
At the same apartment, there was a man living below me who would scream abusively at his girlfriend when she came to stay on the weekend. I never did anything because as far as I could tell, it was just screaming, and I was young. The neighbor next to him would then start pounding on the walls and scream at him to shut up. Well, one day after one of these episodes, he called the police on me for making noise and disturbing him! My boyfriend at the time (husband now) was there that time, and we told the police exactly what was happening and that we weren't making noise at all. They seemed to believe us, and fortunately, he moved out soon after.
Two officers (I can't remember which kind...FBI?) came to our door while doing a security clearance check on our neighbor who was applying for a special security clearance to move to a government job overseas. They had a bunch of questions that we didn't have many answers to, since we didn't know those neighbors well.
One morning when I was in the shower, I heard some banging. I assumed the cat was trying to open the pocket door to the bathroom from our bedroom and didn't think too much about it. When I got out of the shower, I found my slightly shaken 18-year old daughter. She had been sleeping and the police banging on the front door woke her up. When she saw them, she immediately thought that I hadn't come home from my run and they were there to tell her that something had happened to me. Something had happened at the school behind our house, and they were looking to see if we had heard/seen anything.