I lived in a downtown, "hippie" area apartment during the birth of my first son. I told the guy upstairs that I was having him at home, because we chatted occasionally anyway. I didn't tell the girl across the hall, because I didn't really like her.

He was born in the early am - the guy from upstairs left a card taped to the door later than day congratulating us, so he obviously heard, but he knew what was up. It wasn't the kind of neighborhood where anyone called the cops for loud screaming, no matter what the reason.
This time, we are living in a duplex, and I have never even spoken to the people on the other side. Small town, no one in the neighborhood speaks to each other, really very depressing. I don't like it here, but that's another topic for another forum.

Anyway, I think I'm going to let my landlord, who I am cool with, know that we are having the baby here, and let him handle telling the neighbors for me. He's out and about a lot, cutting the grass, fixing things up, so I figure he'll talk to them before I get around to it.